What is (x^2+10x+25)/(x^2-25) ?

The solution to (x^2+10x+25)/(x^2-25) is (x+5)/(x-5)

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simplify (x^2+10x+25)/(x^2-25)

simplify

\frac{x ^{2} + 10 x + 25}{x ^{2} - 25}

\frac{x + 5}{x - 5}

Solution steps

\frac{x ^{2} + 10 x + 25}{x ^{2} - 25}

Factor

x^{2} + 10 x + 25 : (x + 5)^{2}

= \frac{( x + 5 ) ^{2}}{x ^{2} - 25}

Factor

x^{2} - 25 : (x + 5) (x - 5)

= \frac{( x + 5 ) ^{2}}{( x + 5 ) ( x - 5 )}

Apply exponent rule:

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

(x + 5)^{2} = (x + 5) (x + 5)

= \frac{( x + 5 ) ( x + 5 )}{( x + 5 ) ( x - 5 )}

Cancel the common factor:

x + 5

= \frac{x + 5}{x - 5}

\frac{x}{x + 2} + \frac{3}{x + 2}

(4 x^{2} + 8 x - 4) - (3 x^{2} + 6 x - 2)

\frac{5}{8} + \frac{5}{4}

\frac{x + 1}{x ^{2} - 4 x - 5}

(7 + 5 i) (7 - 5 i)

What is (x^2+10x+25)/(x^2-25) ?
The solution to (x^2+10x+25)/(x^2-25) is (x+5)/(x-5)