What is (9x^2-4)/(5x^2-3x-14)*(3x-6)/(3x-2) ?

The solution to (9x^2-4)/(5x^2-3x-14)*(3x-6)/(3x-2) is (3(3x+2))/(5x+7)

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simplify (9x^2-4)/(5x^2-3x-14)*(3x-6)/(3x-2)

simplify

\frac{9 x ^{2} - 4}{5 x ^{2} - 3 x - 14} \cdot \frac{3 x - 6}{3 x - 2}

\frac{3 ( 3 x + 2 )}{5 x + 7}

Solution steps

\frac{9 x ^{2} - 4}{5 x ^{2} - 3 x - 14} \cdot \frac{3 x - 6}{3 x - 2}

Apply the fraction rule:

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

= \frac{( 9 x ^{2} - 4 ) ( 3 x - 6 )}{( 5 x ^{2} - 3 x - 14 ) ( 3 x - 2 )}

Factor

9 x^{2} - 4 : (3 x + 2) (3 x - 2)

= \frac{( 3 x + 2 ) ( 3 x - 2 ) ( 3 x - 6 )}{( 5 x ^{2} - 3 x - 14 ) ( 3 x - 2 )}

Cancel the common factor:

3 x - 2

= \frac{( 3 x + 2 ) ( 3 x - 6 )}{5 x ^{2} - 3 x - 14}

Factor

3 x - 6 : 3 (x - 2)

= \frac{( 3 x + 2 ) \cdot 3 ( x - 2 )}{5 x ^{2} - 3 x - 14}

Factor

5 x^{2} - 3 x - 14 : (5 x + 7) (x - 2)

= \frac{( 3 x + 2 ) \cdot 3 ( x - 2 )}{( 5 x + 7 ) ( x - 2 )}

Cancel the common factor:

x - 2

= \frac{( 3 x + 2 ) \cdot 3}{5 x + 7}

= \frac{3 ( 3 x + 2 )}{5 x + 7}

\frac{6}{x} - \frac{5}{x + 3}

- 1 - x

2 \div \frac{3}{5}

3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3

- i - i

What is (9x^2-4)/(5x^2-3x-14)*(3x-6)/(3x-2) ?
The solution to (9x^2-4)/(5x^2-3x-14)*(3x-6)/(3x-2) is (3(3x+2))/(5x+7)