What is (x^2+3x-10) 6/(3x-6) ?

The solution to (x^2+3x-10) 6/(3x-6) is 2x+10

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simplify (x^2+3x-10) 6/(3x-6)

simplify

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

2 x + 10

Solution steps

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

Cancel

\frac{6}{3 x - 6} : \frac{2}{x - 2}

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

Apply the fraction rule:

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

= \frac{( x ^{2} + 3 x - 10 ) \cdot 2}{x - 2}

Factor

x^{2} + 3 x - 10 : (x - 2) (x + 5)

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

Cancel the common factor:

x - 2

= (x + 5) \cdot 2

Expand

(x + 5) \cdot 2 : 2 x + 10

= 2 x + 10

\frac{x - 5}{4 x + 8} \cdot (12 x^{2} + 32 x + 16)

x (2 x^{2} + 3 x y + y^{2}) - y (5 x^{2} - 2 x y + y^{2})

(7 - 5) (7 + 5)

cot^{2} (x) - cot^{2} (x) cos^{2} (x)

[\frac{2 x - 2 y ^{2} \cdot ( - x ) 2}{( 2 y ^{4} ) 4}] 4