-a4b+a4c+a3b2+2a3bc-2a3c2-2a2b3-a2b2c-a2bc2+a2c3+ab4+2ab3c-ab2c2+2abc3-ac4-b4c+b3c2-2b2c3+bc4 ————————————————————————————————————————————————————————————————————————————————————————————— (a-b)•(b-c)•(c-a) Reformatting the input :
Changes made to your input should not affect the solution:
(1): "c2" was replaced by "c^2". 2 more similar replacement(s).
Step by step solution :Skip Ad Step 1 : c2 Simplify ————— c - a Equation at the end of step 1 : (a2) (b2) c2 ((—————•(a-c))+(—————•(b-a)))+(———•(c-b)) (a-b) (b-c) c-a Step 2 :Equation at the end of step 2 : (a2) (b2) c2•(c-b) ((—————•(a-c))+(—————•(b-a)))+———————— (a-b) (b-c) c-a Step 3 : b2 Simplify ————— b - c Equation at the end of step 3 : (a2) b2 c2•(c-b) ((—————•(a-c))+(———•(b-a)))+———————— (a-b) b-c c-a Step 4 :Equation at the end of step 4 : (a2) b2•(b-a) c2•(c-b) ((—————•(a-c))+————————)+———————— (a-b) b-c c-a Step 5 : a2 Simplify ————— a - b Equation at the end of step 5 : a2 b2•(b-a) c2•(c-b) ((———•(a-c))+————————)+———————— a-b b-c c-a Step 6 :Equation at the end of step 6 : a2•(a-c) b2•(b-a) c2•(c-b) (————————+————————)+———————— a-b b-c c-a Step 7 :Calculating the Least Common Multiple :
7.1 Find the Least Common Multiple
The left denominator is : a-b
The right denominator is : b-c
Number of times each Algebraic Factor appears in the factorization of: Algebraic Factor Left Denominator Right Denominator L.C.M = Max {Left,Right} a-b 101 b-c 011
Least Common Multiple: (a-b) • (b-c)
Calculating Multipliers :
7.2 Calculate multipliers for the two fractions
Denote the Least Common Multiple by L.C.M Denote the Left Multiplier by Left_M Denote the Right Multiplier by Right_M Denote the Left Deniminator by L_Deno Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = b-c
Right_M = L.C.M / R_Deno = a-b
Making Equivalent Fractions :
7.3 Rewrite the two fractions into equivalent fractions
Two fractions are called equivalent if they have the same numeric value.
For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.
To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.
L. Mult. • L. Num. a2 • (a-c) • (b-c) —————————————————— = —————————————————— L.C.M (a-b) • (b-c) R. Mult. • R. Num. b2 • (b-a) • (a-b) —————————————————— = —————————————————— L.C.M (a-b) • (b-c) Adding fractions that have a common denominator :
7.4 Adding up the two equivalent fractions Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
a2 • (a-c) • (b-c) + b2 • (b-a) • (a-b) a3b - a3c - a2b2 - a2bc + a2c2 + 2ab3 - b4 ——————————————————————————————————————— = —————————————————————————————————————————— (a-b) • (b-c) (a - b) • (b - c) Equation at the end of step 7 : (a3b - a3c - a2b2 - a2bc + a2c2 + 2ab3 - b4) c2 • (c - b) ———————————————————————————————————————————— + ———————————— (a - b) • (b - c) c - a Step 8 :Calculating the Least Common Multiple :
8.1 Find the Least Common Multiple
The left denominator is : (a-b) • (b-c)
The right denominator is : c-a
Number of times each Algebraic Factor appears in the factorization of: Algebraic Factor Left Denominator Right Denominator L.C.M = Max {Left,Right} a-b 101 b-c 101 c-a 011
Least Common Multiple: (a-b) • (b-c) • (c-a)
Calculating Multipliers :
8.2 Calculate multipliers for the two fractions
Denote the Least Common Multiple by L.C.M Denote the Left Multiplier by Left_M Denote the Right Multiplier by Right_M Denote the Left Deniminator by L_Deno Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = c-a
Right_M = L.C.M / R_Deno = (a-b)•(b-c)
Making Equivalent Fractions :
8.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. (a3b-a3c-a2b2-a2bc+a2c2+2ab3-b4) • (c-a) —————————————————— = ———————————————————————————————————————— L.C.M (a-b) • (b-c) • (c-a) R. Mult. • R. Num. c2 • (c-b) • (a-b) • (b-c) —————————————————— = —————————————————————————— L.C.M (a-b) • (b-c) • (c-a) Adding fractions that have a common denominator :
Changes made to your input should not affect the solution:
Step by step solution :Skip Ad(1): "c2" was replaced by "c^2". 2 more similar replacement(s).
Step 1 : c2 Simplify ————— c - a Equation at the end of step 1 : (a2) (b2) c2 ((—————•(a-c))+(—————•(b-a)))+(———•(c-b)) (a-b) (b-c) c-a Step 2 :Equation at the end of step 2 : (a2) (b2) c2•(c-b) ((—————•(a-c))+(—————•(b-a)))+———————— (a-b) (b-c) c-a Step 3 : b2 Simplify ————— b - c Equation at the end of step 3 : (a2) b2 c2•(c-b) ((—————•(a-c))+(———•(b-a)))+———————— (a-b) b-c c-a Step 4 :Equation at the end of step 4 : (a2) b2•(b-a) c2•(c-b) ((—————•(a-c))+————————)+———————— (a-b) b-c c-a Step 5 : a2 Simplify ————— a - b Equation at the end of step 5 : a2 b2•(b-a) c2•(c-b) ((———•(a-c))+————————)+———————— a-b b-c c-a Step 6 :Equation at the end of step 6 : a2•(a-c) b2•(b-a) c2•(c-b) (————————+————————)+———————— a-b b-c c-a Step 7 :Calculating the Least Common Multiple :
7.1 Find the Least Common Multiple
Number of times each Algebraic FactorThe left denominator is : a-b
The right denominator is : b-c
appears in the factorization of: Algebraic
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right} a-b 101 b-c 011
Calculating Multipliers :Least Common Multiple:
(a-b) • (b-c)
7.2 Calculate multipliers for the two fractions
Making Equivalent Fractions :Denote the Least Common Multiple by L.C.M
Denote the Left Multiplier by Left_M
Denote the Right Multiplier by Right_M
Denote the Left Deniminator by L_Deno
Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = b-c
Right_M = L.C.M / R_Deno = a-b
7.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. a2 • (a-c) • (b-c) —————————————————— = —————————————————— L.C.M (a-b) • (b-c) R. Mult. • R. Num. b2 • (b-a) • (a-b) —————————————————— = —————————————————— L.C.M (a-b) • (b-c) Adding fractions that have a common denominator :Two fractions are called equivalent if they have the same numeric value.
For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.
To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.
7.4 Adding up the two equivalent fractions
a2 • (a-c) • (b-c) + b2 • (b-a) • (a-b) a3b - a3c - a2b2 - a2bc + a2c2 + 2ab3 - b4 ——————————————————————————————————————— = —————————————————————————————————————————— (a-b) • (b-c) (a - b) • (b - c) Equation at the end of step 7 : (a3b - a3c - a2b2 - a2bc + a2c2 + 2ab3 - b4) c2 • (c - b) ———————————————————————————————————————————— + ———————————— (a - b) • (b - c) c - a Step 8 :Calculating the Least Common Multiple :Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
8.1 Find the Least Common Multiple
Number of times each Algebraic FactorThe left denominator is : (a-b) • (b-c)
The right denominator is : c-a
appears in the factorization of: Algebraic
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right} a-b 101 b-c 101 c-a 011
Calculating Multipliers :Least Common Multiple:
(a-b) • (b-c) • (c-a)
8.2 Calculate multipliers for the two fractions
Making Equivalent Fractions :Denote the Least Common Multiple by L.C.M
Denote the Left Multiplier by Left_M
Denote the Right Multiplier by Right_M
Denote the Left Deniminator by L_Deno
Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = c-a
Right_M = L.C.M / R_Deno = (a-b)•(b-c)
8.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. (a3b-a3c-a2b2-a2bc+a2c2+2ab3-b4) • (c-a) —————————————————— = ———————————————————————————————————————— L.C.M (a-b) • (b-c) • (c-a) R. Mult. • R. Num. c2 • (c-b) • (a-b) • (b-c) —————————————————— = —————————————————————————— L.C.M (a-b) • (b-c) • (c-a) Adding fractions that have a common denominator :8.4 Adding up the two equivalent fractions
(a3b-a3c-a2b2-a2bc+a2c2+2ab3-b4) • (c-a) + c2 • (c-b) • (a-b) • (b-c) -a4b+a4c+a3b2+2a3bc-2a3c2-2a2b3-a2b2c-a2bc2+a2c3+ab4+2ab3c-ab2c2+2abc3-ac4-b4c+b3c2-2b2c3+bc4 ————————————————————————————————————————————————————————————————————— = ————————————————————————————————————————————————————————————————————————————————————————————— (a-b) • (b-c) • (c-a) (a-b) • (b-c) • (c-a) Final result : -a4b+a4c+a3b2+2a3bc-2a3c2-2a2b3-a2b2c-a2bc2+a2c3+ab4+2ab3c-ab2c2+2abc3-ac4-b4c+b3c2-2b2c3+bc4 ————————————————————————————————————————————————————————————————————————————————————————————— (a-b)•(b-c)•(c-a)
Latest drills solved(-4,7)to(94,-55)(5)/(7)+(4)/(y)=38(x+8/9)-9a2/(a-b)(a-c)+b2/(b-c)(b-a)+c2/(c-a)(c-b)Processing ends successfully