What is 8/(y^2-16)-7/(y^2-y-12) ?

The solution to 8/(y^2-16)-7/(y^2-y-12) is 1/((y+4)(y+3))

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simplify 8/(y^2-16)-7/(y^2-y-12)

simplify

\frac{8}{y ^{2} - 16} - \frac{7}{y ^{2} - y - 12}

\frac{1}{( y + 4 ) ( y + 3 )}

Solution steps

\frac{8}{y ^{2} - 16} - \frac{7}{y ^{2} - y - 12}

Least Common Multiplier of

y^{2} - 16, y^{2} - y - 12 : (y + 4) (y - 4) (y + 3)

Adjust Fractions based on the LCM

= \frac{8 ( y + 3 )}{( y + 4 ) ( y - 4 ) ( y + 3 )} - \frac{7 ( y + 4 )}{( y + 4 ) ( y - 4 ) ( y + 3 )}

Apply the fraction rule:

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

= \frac{8 ( y + 3 ) - 7 ( y + 4 )}{( y + 4 ) ( y - 4 ) ( y + 3 )}

Simplify

8 (y + 3) - 7 (y + 4) : y - 4

= \frac{y - 4}{( y + 4 ) ( y - 4 ) ( y + 3 )}

Cancel the common factor:

y - 4

= \frac{1}{( y + 4 ) ( y + 3 )}

x^{2} - 9 + x + 3

\frac{4}{50}

+ 9 u^{2} - 80 u - 9

(- 6 x^{5})^{2}

What is 8/(y^2-16)-7/(y^2-y-12) ?
The solution to 8/(y^2-16)-7/(y^2-y-12) is 1/((y+4)(y+3))