1/(a+b)-1/(a-b)

This solution deals with adding, subtracting and finding the least common multiple.




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Step by Step Solution

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Step 1 :

1 Simplify ————— a - bEquation at the kết thúc of step 1 : 1 1 ——————— - ————— (a + b) a - b

Step 2 :

1 Simplify ————— a + bEquation at the kết thúc of step 2 : 1 1 ————— - ————— a + b a - b

Step 3 :

Calculating the Least Common Multiple :3.1 Find the Least Common Multiple The left denominator is : a+b The right denominator is : a-b

Number of times each Algebraic Factorappears in the factorization of:AlgebraicFactorLeftDenominatorRightDenominatorL.C.M = MaxLeft,Right
a+b101
a-b011

Least Common Multiple: (a+b)•(a-b)

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_DenoLeft_M=L.C.M/L_Deno=a-bRight_M=L.C.M/R_Deno=a+b

Making Equivalent Fractions :

3.3 Rewrite the two fractions into equivalent fractionsTwo fractions are called equivalent if they have the same numeric value. For example : một nửa and 2/4 are equivalent, y/(y+1)2 và (y2+y)/(y+1)3 are equivalent as well. Khổng lồ calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

L. Mult. • L. Num. A-b —————————————————— = ————————————— L.C.M (a+b) • (a-b) R. Mult. • R.

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Num. A+b —————————————————— = ————————————— L.C.M (a+b) • (a-b)Adding fractions that have a common denominator :3.4 Adding up the two equivalent fractions showroom the two equivalent fractions which now have a common denominatorCombine the numerators together, put the sum or difference over the common denominator then reduce khổng lồ lowest terms if possible:

a-b - (a+b) -2b ————————————— = ————————————————— (a+b) • (a-b) (a + b) • (a - b)

Final result :

-2b ————————————————— (a + b) • (a - b)