What is (x^2+3x-10)/(6x^2-18x)*(6x^2+24x-126)/(x^2+12x+35) ?

The solution to (x^2+3x-10)/(6x^2-18x)*(6x^2+24x-126)/(x^2+12x+35) is (x-2)/x

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simplify (x^2+3x-10)/(6x^2-18x)*(6x^2+24x-126)/(x^2+12x+35)

simplify

\frac{x ^{2} + 3 x - 10}{6 x ^{2} - 18 x} \cdot \frac{6 x ^{2} + 24 x - 126}{x ^{2} + 12 x + 35}

\frac{x - 2}{x}

Solution steps

\frac{x ^{2} + 3 x - 10}{6 x ^{2} - 18 x} \cdot \frac{6 x ^{2} + 24 x - 126}{x ^{2} + 12 x + 35}

Cancel

\frac{6 x ^{2} + 24 x - 126}{x ^{2} + 12 x + 35} : \frac{6 ( x - 3 )}{x + 5}

= \frac{x ^{2} + 3 x - 10}{6 x ^{2} - 18 x} \cdot \frac{6 ( x - 3 )}{x + 5}

Apply the fraction rule:

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

= \frac{( x ^{2} + 3 x - 10 ) \cdot 6 ( x - 3 )}{( 6 x ^{2} - 18 x ) ( x + 5 )}

Factor

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

= \frac{( x - 2 ) ( x + 5 ) \cdot 6 ( x - 3 )}{( 6 x ^{2} - 18 x ) ( x + 5 )}

Cancel the common factor:

x + 5

= \frac{( x - 2 ) \cdot 6 ( x - 3 )}{6 x ^{2} - 18 x}

Factor

6 x^{2} - 18 x : 6 x (x - 3)

= \frac{( x - 2 ) \cdot 6 ( x - 3 )}{6 x ( x - 3 )}

Cancel the common factor:

6

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

Cancel the common factor:

x - 3

= \frac{x - 2}{x}

2 x^{3} - 3 x + 1

2 x (x + 5)

\frac{( 2 h ^{4} ) ^{5}}{6 h ^{6}}

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

x^{3} + 5 x^{2} + 7 x + 3

What is (x^2+3x-10)/(6x^2-18x)*(6x^2+24x-126)/(x^2+12x+35) ?
The solution to (x^2+3x-10)/(6x^2-18x)*(6x^2+24x-126)/(x^2+12x+35) is (x-2)/x