What is (x^2+6x+9)/(x^2+2x-3) ?

The solution to (x^2+6x+9)/(x^2+2x-3) is (x+3)/(x-1)

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simplify (x^2+6x+9)/(x^2+2x-3)

simplify

\frac{x ^{2} + 6 x + 9}{x ^{2} + 2 x - 3}

\frac{x + 3}{x - 1}

Solution steps

\frac{x ^{2} + 6 x + 9}{x ^{2} + 2 x - 3}

Factor

x^{2} + 6 x + 9 : (x + 3)^{2}

= \frac{( x + 3 ) ^{2}}{x ^{2} + 2 x - 3}

Factor

x^{2} + 2 x - 3 : (x - 1) (x + 3)

= \frac{( x + 3 ) ^{2}}{( x - 1 ) ( x + 3 )}

Apply exponent rule:

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

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

= \frac{( x + 3 ) ( x + 3 )}{( x - 1 ) ( x + 3 )}

Cancel the common factor:

x + 3

= \frac{x + 3}{x - 1}

(3 x - 2)^{4}

27 x^{4}

(4 x + 8)^{2}

(\times + 3)^{2}

\frac{x ^{2} + 5 x + 4}{x ^{2} + 2 x - 8}

What is (x^2+6x+9)/(x^2+2x-3) ?
The solution to (x^2+6x+9)/(x^2+2x-3) is (x+3)/(x-1)