What is (x+2)/(x^2+14x+49)*(x^2+6x-7)/(x^2+x-2) ?

The solution to (x+2)/(x^2+14x+49)*(x^2+6x-7)/(x^2+x-2) is 1/(x+7)

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simplify (x+2)/(x^2+14x+49)*(x^2+6x-7)/(x^2+x-2)

simplify

\frac{x + 2}{x ^{2} + 14 x + 49} \cdot \frac{x ^{2} + 6 x - 7}{x ^{2} + x - 2}

\frac{1}{x + 7}

Solution steps

\frac{x + 2}{x ^{2} + 14 x + 49} \cdot \frac{x ^{2} + 6 x - 7}{x ^{2} + x - 2}

Cancel

\frac{x ^{2} + 6 x - 7}{x ^{2} + x - 2} : \frac{x + 7}{x + 2}

= \frac{x + 2}{x ^{2} + 14 x + 49} \cdot \frac{x + 7}{x + 2}

Cross-cancel common factor:

x + 2

= \frac{x + 7}{x ^{2} + 14 x + 49}

Factor

x^{2} + 14 x + 49 : (x + 7)^{2}

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

Apply exponent rule:

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

(x + 7)^{2} = (x + 7) (x + 7)

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

Cancel the common factor:

x + 7

= \frac{1}{x + 7}

e^{3 i}

(3 x^{2} + 4 x y^{7})^{2}

(3 x^{2} + 2 x)^{3}

245 e^{0.15}

\frac{7}{30}

What is (x+2)/(x^2+14x+49)*(x^2+6x-7)/(x^2+x-2) ?
The solution to (x+2)/(x^2+14x+49)*(x^2+6x-7)/(x^2+x-2) is 1/(x+7)