What is (4x^2+10)/(x-3)*(x^2-9)/(6x^2+15) ?

The solution to (4x^2+10)/(x-3)*(x^2-9)/(6x^2+15) is (2(x+3))/3

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simplify (4x^2+10)/(x-3)*(x^2-9)/(6x^2+15)

simplify

\frac{4 x ^{2} + 10}{x - 3} \cdot \frac{x ^{2} - 9}{6 x ^{2} + 15}

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

Solution steps

\frac{4 x ^{2} + 10}{x - 3} \cdot \frac{x ^{2} - 9}{6 x ^{2} + 15}

Apply the fraction rule:

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

= \frac{( 4 x ^{2} + 10 ) ( x ^{2} - 9 )}{( x - 3 ) ( 6 x ^{2} + 15 )}

Factor

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

= \frac{( 4 x ^{2} + 10 ) ( x + 3 ) ( x - 3 )}{( x - 3 ) ( 6 x ^{2} + 15 )}

Cancel the common factor:

x - 3

= \frac{( 4 x ^{2} + 10 ) ( x + 3 )}{6 x ^{2} + 15}

Factor

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

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

Factor

6 x^{2} + 15 : 3 (2 x^{2} + 5)

= \frac{2 ( 2 x ^{2} + 5 ) ( x + 3 )}{3 ( 2 x ^{2} + 5 )}

Cancel the common factor:

2 x^{2} + 5

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

(- 8) + (- 5)

\frac{2}{6} + \frac{1}{4}

(7 x - 2 y)^{2}

\frac{8 x ^{3}}{10 x ^{5}}

- - 76

What is (4x^2+10)/(x-3)*(x^2-9)/(6x^2+15) ?
The solution to (4x^2+10)/(x-3)*(x^2-9)/(6x^2+15) is (2(x+3))/3