What is (\frac{2x^2+3x+1)/(x^2+2x-15)}{(x^2+6x+5)/(2x^2-7x+3)} ?

The solution to (\frac{2x^2+3x+1)/(x^2+2x-15)}{(x^2+6x+5)/(2x^2-7x+3)} is ((2x+1)(2x-1))/((x+5)^2)

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simplify (\frac{2x^2+3x+1)/(x^2+2x-15)}{(x^2+6x+5)/(2x^2-7x+3)}

simplify

\frac{\frac{2 x ^{2} + 3 x + 1}{x ^{2} + 2 x - 15}}{\frac{x ^{2} + 6 x + 5}{2 x ^{2} - 7 x + 3}}

\frac{( 2 x + 1 ) ( 2 x - 1 )}{( x + 5 ) ^{2}}

Solution steps

\frac{\frac{2 x ^{2} + 3 x + 1}{x ^{2} + 2 x - 15}}{\frac{x ^{2} + 6 x + 5}{2 x ^{2} - 7 x + 3}}

Apply the fraction rule:

\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a \cdot d}{b \cdot c}

= \frac{( 2 x ^{2} + 3 x + 1 ) ( 2 x ^{2} - 7 x + 3 )}{( x ^{2} + 2 x - 15 ) ( x ^{2} + 6 x + 5 )}

Cancel

\frac{( 2 x ^{2} + 3 x + 1 ) ( 2 x ^{2} - 7 x + 3 )}{( x ^{2} + 2 x - 15 ) ( x ^{2} + 6 x + 5 )} : \frac{( 2 x + 1 ) ( 2 x - 1 )}{( x + 5 ) ^{2}}

= \frac{( 2 x + 1 ) ( 2 x - 1 )}{( x + 5 ) ^{2}}

\frac{x ^{2} - 8 x + 16}{x ^{2} - 16}

\frac{1}{4} - \frac{2}{5}

(y + 1) (y - 1)

- m - n + x (m + n)

5 - 11

What is (\frac{2x^2+3x+1)/(x^2+2x-15)}{(x^2+6x+5)/(2x^2-7x+3)} ?
The solution to (\frac{2x^2+3x+1)/(x^2+2x-15)}{(x^2+6x+5)/(2x^2-7x+3)} is ((2x+1)(2x-1))/((x+5)^2)