a+b-c/(a-b)(b-c)+b+c-a/(b-c)(c-a)+c+a-b/(c-a)(c-b)
Answers
Answer:(b+c-a)/((a-b)(a-c))+(c+a-b)/((b-c)(b-a))+(a+b-c)/((c-a)(c-b))
Final result :
0
Step by step solution :
Step 1 :
Equation at the end of step 1 :
(b+c-a) (-b+c+a) (b-c+a)
(—————————————+—————————————)+———————————
((a-b)•(a-c)) ((b-c)•(b-a)) (c-a)•(c-b)
Step 2 :
b - c + a
Simplify —————————————————
(c - a) • (c - b)
Equation at the end of step 2 :
(b+c-a) (-b+c+a) (b-c+a)
(—————————————+—————————————)+———————————
((a-b)•(a-c)) ((b-c)•(b-a)) (c-a)•(c-b)
Step 3 :
Equation at the end of step 3 :
(b+c-a) (-b+c+a) (b-c+a)
(—————————————+———————————)+———————————
((a-b)•(a-c)) (b-c)•(b-a) (c-a)•(c-b)
Step 4 :
-b + c + a
Simplify —————————————————
(b - c) • (b - a)
Equation at the end of step 4 :
(b+c-a) (-b+c+a) (b-c+a)
(—————————————+———————————)+———————————
((a-b)•(a-c)) (b-c)•(b-a) (c-a)•(c-b)
Step 5 :
Equation at the end of step 5 :
(b+c-a) (-b+c+a) (b-c+a)
(———————————+———————————)+———————————
(a-b)•(a-c) (b-c)•(b-a) (c-a)•(c-b)
Step 6 :
b + c - a
Simplify —————————————————
(a - b) • (a - c)
Equation at the end of step 6 :
(b+c-a) (-b+c+a) (b-c+a)
(———————————+———————————)+———————————
(a-b)•(a-c) (b-c)•(b-a) (c-a)•(c-b)
Step 7 :
Calculating the Least Common Multiple :
7.1 Find the Least Common Multiple
The left denominator is : (a-b) • (a-c)
The right denominator is : (b-c) • (b-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
1
1
1
a-c
1
0
1
b-c
0
1
1
Least Common Multiple:
(a-b) • (a-c) • (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 = -1•(a-c)
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. (b+c-a) • (b-c)
—————————————————— = —————————————————————
L.C.M (a-b) • (a-c) • (b-c)
R. Mult. • R. Num. (-b+c+a) • -1 • (a-c)
—————————————————— = —————————————————————
L.C.M (a-b) • (a-c) • (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:
(b+c-a) • (b-c) + (-b+c+a) • -1 • (a-c) b2 - bc + ca - a2
——————————————————————————————————————— = ———————————————————————————
(a-b) • (a-c) • (b-c) (a - b) • (a - c) • (b - c)
Equation at the end of step 7 :
(b2-bc+ca-a2) (b-c+a)
—————————————————+———————————
(a-b)•(a-c)•(b-c) (c-a)•(c-b)
Step 8 :
Calculating the Least Common Multiple :
8.1 Find the Least Common Multiple
The left denominator is : (a-b) • (a-c) • (b-c)
The right denominator is : (c-a) • (c-b)
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
1
0
1
a-c
1
1
1
b-c
1
1
1
Least Common Multiple:
(a-b) • (a-c) • (b-c)
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 = 1
Right_M = L.C.M / R_Deno = (a-b)•-1•-1
Making Equivalent Fractions :
8.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. (b2-bc+ca-a2)
—————————————————— = —————————————————————
L.C.M (a-b) • (a-c) • (b-c)
R. Mult. • R. Num. (b-c+a) • (a-b) • -1 • -1
—————————————————— = —————————————————————————
L.C.M (a-b) • (a-c) • (b-c)
Adding fractions that have a common denominator :
8.4 Adding up the two equivalent fractions
(b2-bc+ca-a2) + (b-c+a) • (a-b) • -1 • -1 0
————————————————————————————————————————— = ———————————————————————————
(a-b) • (a-c) • (b-c) (a - b) • (a - c) • (b - c)
Final result :
0
Processing ends successfully
Step-by-step explanation:
Answer
find the lowest common denominator of (a/b+c)/(a/b-c)
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