What is (y-3)/((y-5)^2)-(y-2)/(y^2-4y-5) ?

The solution to (y-3)/((y-5)^2)-(y-2)/(y^2-4y-5) is (5y-13)/((y-5)^2(y+1))

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simplify (y-3)/((y-5)^2)-(y-2)/(y^2-4y-5)

simplify

\frac{y - 3}{( y - 5 ) ^{2}} - \frac{y - 2}{y ^{2} - 4 y - 5}

\frac{5 y - 13}{( y - 5 ) ^{2} ( y + 1 )}

Solution steps

\frac{y - 3}{( y - 5 ) ^{2}} - \frac{y - 2}{y ^{2} - 4 y - 5}

Least Common Multiplier of

(y - 5)^{2}, y^{2} - 4 y - 5 : (y - 5)^{2} (y + 1)

Adjust Fractions based on the LCM

= \frac{( y - 3 ) ( y + 1 )}{( y - 5 ) ^{2} ( y + 1 )} - \frac{( y - 2 ) ( y - 5 )}{( y - 5 ) ^{2} ( y + 1 )}

Apply the fraction rule:

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

= \frac{( y - 3 ) ( y + 1 ) - ( y - 2 ) ( y - 5 )}{( y - 5 ) ^{2} ( y + 1 )}

Simplify

(y - 3) (y + 1) - (y - 2) (y - 5) : 5 y - 13

= \frac{5 y - 13}{( y - 5 ) ^{2} ( y + 1 )}

\frac{5}{4 x + 8} - \frac{- 5}{- 3 x - 5}

\frac{3}{2} - \frac{4}{5}

16 x^{2} + 40 x y^{3} + 25 y^{6}

\frac{1}{2} \cdot \frac{3}{2}

4 \div \frac{1}{9}

What is (y-3)/((y-5)^2)-(y-2)/(y^2-4y-5) ?
The solution to (y-3)/((y-5)^2)-(y-2)/(y^2-4y-5) is (5y-13)/((y-5)^2(y+1))