What is (3a-b)/(a^2-b^2)+1/(a-b) ?

The solution to (3a-b)/(a^2-b^2)+1/(a-b) is (4a)/(a^2-b^2)

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simplify (3a-b)/(a^2-b^2)+1/(a-b)

simplify

\frac{3 a - b}{a ^{2} - b ^{2}} + \frac{1}{a - b}

\frac{4 a}{a ^{2} - b ^{2}}

Solution steps

\frac{3 a - b}{a ^{2} - b ^{2}} + \frac{1}{a - b}

Least Common Multiplier of

a^{2} - b^{2}, a - b : (a - b) (a^{2} - b^{2})

Adjust Fractions based on the LCM

= \frac{( 3 a - b ) ( a - b )}{( a - b ) ( a ^{2} - b ^{2} )} + \frac{a ^{2} - b ^{2}}{( a - b ) ( a ^{2} - b ^{2} )}

Apply the fraction rule:

\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}

= \frac{( 3 a - b ) ( a - b ) + a ^{2} - b ^{2}}{( a - b ) ( a ^{2} - b ^{2} )}

Simplify

(3 a - b) (a - b) + a^{2} - b^{2} : 4 a^{2} - 4 ab

= \frac{4 a ^{2} - 4 ab}{( a - b ) ( a ^{2} - b ^{2} )}

Cancel

\frac{4 a ^{2} - 4 ab}{( a - b ) ( a ^{2} - b ^{2} )} : \frac{4 a}{a ^{2} - b ^{2}}

= \frac{4 a}{a ^{2} - b ^{2}}

∣ 5 y + 2 ∣ > 0

5 x - 3 > 0

5 k^{2} + 13 k - 6

10 y^{2} - 3 y (x - 2 y) - (x - 2 y)^{2}

3 x^{2} \leq x (x + 1)

What is (3a-b)/(a^2-b^2)+1/(a-b) ?
The solution to (3a-b)/(a^2-b^2)+1/(a-b) is (4a)/(a^2-b^2)