What is (175-7k^2)/(k^2+7k-60) ?

The solution to (175-7k^2)/(k^2+7k-60) is -(7(5+k))/(k+12)

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simplify (175-7k^2)/(k^2+7k-60)

simplify

\frac{175 - 7 k ^{2}}{k ^{2} + 7 k - 60}

- \frac{7 ( 5 + k )}{k + 12}

Solution steps

\frac{175 - 7 k ^{2}}{k ^{2} + 7 k - 60}

Factor

175 - 7 k^{2} : 7 (5 + k) (5 - k)

= \frac{7 ( 5 + k ) ( 5 - k )}{k ^{2} + 7 k - 60}

Factor

k^{2} + 7 k - 60 : (k - 5) (k + 12)

= \frac{7 ( 5 + k ) ( 5 - k )}{( k - 5 ) ( k + 12 )}

7 (5 + k) (5 - k) = - 7 (5 + k) (k - 5)

= \frac{- 7 ( 5 + k ) ( k - 5 )}{( k - 5 ) ( k + 12 )}

Cancel the common factor:

k - 5

= \frac{- 7 ( 5 + k )}{k + 12}

Apply the fraction rule:

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

= - \frac{7 ( 5 + k )}{k + 12}

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What is (175-7k^2)/(k^2+7k-60) ?
The solution to (175-7k^2)/(k^2+7k-60) is -(7(5+k))/(k+12)