simplify (xa/xb)a X (xb/xa)b X (xa/xa)b
Answers
Answer:
(x-a)/(x-b)+(x-b)/(x-a)=a/b+b/a
One solution was found :
x = 0
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
(x-a)/(x-b)+(x-b)/(x-a)-(a/b+b/a)=0
Step by step solution :
Step 1 :
b
Simplify —
a
Equation at the end of step 1 :
(x-a) (x-b) a b
(—————+—————)-(—+—) = 0
(x-b) (x-a) b a
Step 2 :
a
Simplify —
b
Equation at the end of step 2 :
(x-a) (x-b) a b
(—————+—————)-(—+—) = 0
(x-b) (x-a) b a
Step 3 :
Calculating the Least Common Multiple :
3.1 Find the Least Common Multiple
The left denominator is : b
The right denominator is : 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 0 1 1
b 1 0 1
Least Common Multiple:
ab
Calculating Multipliers :
3.2 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 = a
Right_M = L.C.M / R_Deno = b
Making Equivalent Fractions :
3.3 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. a • a
—————————————————— = —————
L.C.M ab
R. Mult. • R. Num. b • b
—————————————————— = —————
L.C.M ab
Adding fractions that have a common denominator :
3.4 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:
a • a + b • b a2 + b2
————————————— = ———————
ab ab
Equation at the end of step 3 :
(x-a) (x-b) (a2+b2)
(—————+—————)-——————— = 0
(x-b) (x-a) ab
Step 4 :
x - b
Simplify —————
x - a
Equation at the end of step 4 :
(x - a) (x - b) (a2 + b2)
(——————— + ———————) - ————————— = 0
(x - b) x - a ab
Step 5 :
x - a
Simplify —————
x - b
Equation at the end of step 5 :
(x - a) (x - b) (a2 + b2)
(——————— + ———————) - ————————— = 0
x - b x - a ab
Step 6 :
Calculating the Least Common Multiple :
6.1 Find the Least Common Multiple
The left denominator is : x-b
The right denominator is : x-a
Number of times each Algebraic Factor
appears in the factorization of:
Algebraic
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
x-b 1 0 1
x-a 0 1 1
Least Common Multiple:
(x-b) • (x-a)
Calculating Multipliers :
6.2 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 = x-a
Right_M = L.C.M / R_Deno = x-b
Making Equivalent Fractions :
6.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. (x-a) • (x-a)
—————————————————— = —————————————
L.C.M (x-b) • (x-a)
R. Mult. • R. Num. (x-b) • (x-b)
—————————————————— = —————————————
L.C.M (x-b) • (x-a)
Adding fractions that have a common denominator :
6.4 Adding up the two equivalent fractions
(x-a) • (x-a) + (x-b) • (x-b) 2x2 - 2xa - 2xb + a2 + b2
————————————————————————————— = —————————————————————————
(x-b) • (x-a) (x - b) • (x - a)
Equation at the end of step 6 :
(2x2 - 2xa - 2xb + a2 + b2) (a2 + b2)
——————————————————————————— - ————————— = 0
(x - b) • (x - a) ab
Step 7 :
Calculating the Least Common Multiple :
7.1 Find the Least Common Multiple
The left denominator is : (x-b) • (x-a)
The right denominator is : ab
Number of times each Algebraic Factor
appears in the factorization of:
Algebraic
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
a 0 1 1
b 0 1 1
x-b 1 0 1
x-a 1 0 1
Least Common Multiple:
ab • (x-b) • (x-a)
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
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