What is (a^2-a-90)/(100-a^2) ?

The solution to (a^2-a-90)/(100-a^2) is -(a+9)/(10+a)

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simplify (a^2-a-90)/(100-a^2)

simplify

\frac{a ^{2} - a - 90}{100 - a ^{2}}

- \frac{a + 9}{10 + a}

Solution steps

\frac{a ^{2} - a - 90}{100 - a ^{2}}

Factor

a^{2} - a - 90 : (a + 9) (a - 10)

= \frac{( a + 9 ) ( a - 10 )}{100 - a ^{2}}

Factor

100 - a^{2} : (10 + a) (10 - a)

= \frac{( a + 9 ) ( a - 10 )}{( 10 + a ) ( 10 - a )}

(10 + a) (10 - a) = - (10 + a) (a - 10)

= \frac{( a + 9 ) ( a - 10 )}{- ( 10 + a ) ( a - 10 )}

Cancel the common factor:

a - 10

= \frac{a + 9}{- ( 10 + a )}

Apply the fraction rule:

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

= - \frac{a + 9}{10 + a}

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What is (a^2-a-90)/(100-a^2) ?
The solution to (a^2-a-90)/(100-a^2) is -(a+9)/(10+a)