What is (x^2-5x-14)/(x^2+4x+4) ?

The solution to (x^2-5x-14)/(x^2+4x+4) is (x-7)/(x+2)

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simplify (x^2-5x-14)/(x^2+4x+4)

simplify

\frac{x ^{2} - 5 x - 14}{x ^{2} + 4 x + 4}

\frac{x - 7}{x + 2}

Solution steps

\frac{x ^{2} - 5 x - 14}{x ^{2} + 4 x + 4}

Factor

x^{2} - 5 x - 14 : (x + 2) (x - 7)

= \frac{( x + 2 ) ( x - 7 )}{x ^{2} + 4 x + 4}

Factor

x^{2} + 4 x + 4 : (x + 2)^{2}

= \frac{( x + 2 ) ( x - 7 )}{( x + 2 ) ^{2}}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

(x + 2)^{2} = (x + 2) (x + 2)

= \frac{( x + 2 ) ( x - 7 )}{( x + 2 ) ( x + 2 )}

Cancel the common factor:

x + 2

= \frac{x - 7}{x + 2}

x^{2} - 20 x + 36

(2 + 3 x)^{3}

- 2 x (x + 1) (5 - 2 x)

\frac{2}{3} x^{2}

(16 - x)^{2}

What is (x^2-5x-14)/(x^2+4x+4) ?
The solution to (x^2-5x-14)/(x^2+4x+4) is (x-7)/(x+2)