<span>-a4b+a4c+a3b2+2a3bc-2a3c2-2a2b3-a2b2c-a2bc2+a2c3+ab4+2ab3c-ab2c2+2abc3-ac4-b4c+b3c2-2b2c3+bc4
—————————————————————————————————————————————————————————————————————————————————————————————
(a-b)•(b-c)•(c-a)
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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
<span>Step 1 :</span><span> c2
Simplify —————
c - a
</span><span>Equation at the end of step 1 :</span><span> (a2) (b2) c2
((—————•(a-c))+(—————•(b-a)))+(———•(c-b))
(a-b) (b-c) c-a
</span><span>Step 2 :</span><span>Equation at the end of step 2 :</span><span><span> (a2) (b2) c2•(c-b)
((—————•(a-c))+(—————•(b-a)))+————————
(a-b) (b-c) c-a
</span><span> Step 3 :</span><span> b2
Simplify —————
b - c
</span></span><span>Equation at the end of step 3 :</span><span> (a2) b2 c2•(c-b)
((—————•(a-c))+(———•(b-a)))+————————
(a-b) b-c c-a
</span><span>Step 4 :</span><span>Equation at the end of step 4 :</span><span><span> (a2) b2•(b-a) c2•(c-b)
((—————•(a-c))+————————)+————————
(a-b) b-c c-a
</span><span> Step 5 :</span><span> a2
Simplify —————
a - b
</span></span><span>Equation at the end of step 5 :</span><span> a2 b2•(b-a) c2•(c-b)
((———•(a-c))+————————)+————————
a-b b-c c-a
</span><span>Step 6 :</span><span>Equation at the end of step 6 :</span><span> a2•(a-c) b2•(b-a) c2•(c-b)
(————————+————————)+————————
a-b b-c c-a
</span><span>Step 7 :</span>Calculating the Least Common Multiple :
<span> 7.1 </span> Find the Least Common Multiple
The left denominator is : <span> a-b </span>
The right denominator is : <span> b-c </span>
<span><span> Number of times each Algebraic Factor
appears in the factorization of:</span><span><span><span> Algebraic
Factor </span><span> Left
Denominator </span><span> Right
Denominator </span><span> L.C.M = Max
{Left,Right} </span></span><span><span> a-b </span>101</span><span><span> b-c </span>011</span></span></span>
Least Common Multiple:
(a-b) • (b-c)
Calculating Multipliers :
<span> 7.2 </span> 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 :
<span> 7.3 </span> Rewrite the two fractions into<span> equivalent fractions</span>
Two fractions are called <span>equivalent </span>if they have the<span> same numeric value.</span>
For example : 1/2 and 2/4 are equivalent, <span> y/(y+1)2 </span> and <span> (y2+y)/(y+1)3 </span>are equivalent as well.
To calculate equivalent fraction , multiply the <span>Numerator </span>of each fraction, by its respective Multiplier.
<span><span> L. Mult. • L. Num. a2 • (a-c) • (b-c)
—————————————————— = ——————————————————
L.C.M (a-b) • (b-c)
</span><span> R. Mult. • R. Num. b2 • (b-a) • (a-b)
—————————————————— = ——————————————————
L.C.M (a-b) • (b-c)
</span></span>Adding fractions that have a common denominator :
<span> 7.4 </span> 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:
<span> 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)
</span><span>Equation at the end of step 7 :</span><span> (a3b - a3c - a2b2 - a2bc + a2c2 + 2ab3 - b4) c2 • (c - b)
———————————————————————————————————————————— + ————————————
(a - b) • (b - c) c - a
</span><span>Step 8 :</span>Calculating the Least Common Multiple :
<span> 8.1 </span> Find the Least Common Multiple
The left denominator is : <span> (a-b) •</span> (b-c)
The right denominator is : <span> c-a </span>
<span><span> Number of times each Algebraic Factor
appears in the factorization of:</span><span><span><span> Algebraic
Factor </span><span> Left
Denominator </span><span> Right
Denominator </span><span> L.C.M = Max
{Left,Right} </span></span><span><span> a-b </span>101</span><span><span> b-c </span>101</span><span><span> c-a </span>011</span></span></span>
Least Common Multiple:
(a-b) • (b-c) • (c-a)
Calculating Multipliers :
<span> 8.2 </span> 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 :
<span> 8.3 </span> Rewrite the two fractions into<span> equivalent fractions</span>
<span><span> L. Mult. • L. Num. (a3b-a3c-a2b2-a2bc+a2c2+2ab3-b4) • (c-a)
—————————————————— = ————————————————————————————————————————
L.C.M (a-b) • (b-c) • (c-a)
</span><span> R. Mult. • R. Num. c2 • (c-b) • (a-b) • (b-c)
—————————————————— = ——————————————————————————
L.C.M (a-b) • (b-c) • (c-a)
</span></span>Adding fractions that have a common denominator :
<span> 8.4 </span> Adding up the two equivalent fractions
<span> (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)
</span>Final result :<span> -a4b+a4c+a3b2+2a3bc-2a3c2-2a2b3-a2b2c-a2bc2+a2c3+ab4+2ab3c-ab2c2+2abc3-ac4-b4c+b3c2-2b2c3+bc4
—————————————————————————————————————————————————————————————————————————————————————————————
(a-b)•(b-c)•(c-a)
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Processing ends successfully</span>
Latest drills solved<span>(-4,7)to(94,-55)(5)/(7)+(4)/(y)=3<span>8(x+8/9)-9</span></span><span><span>a2/(a-b)(a-c)+b2/(b-c)(b-a)+c2/(c-a)(c-b)</span>
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