What is (6x^3+42x^2)/(2x^2+26x+84) ?

The solution to (6x^3+42x^2)/(2x^2+26x+84) is (3x^2)/(x+6)

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simplify (6x^3+42x^2)/(2x^2+26x+84)

simplify

\frac{6 x ^{3} + 42 x ^{2}}{2 x ^{2} + 26 x + 84}

\frac{3 x ^{2}}{x + 6}

Solution steps

\frac{6 x ^{3} + 42 x ^{2}}{2 x ^{2} + 26 x + 84}

Factor

6 x^{3} + 42 x^{2} : 6 x^{2} (x + 7)

= \frac{6 x ^{2} ( x + 7 )}{2 x ^{2} + 26 x + 84}

Factor

2 x^{2} + 26 x + 84 : 2 (x + 6) (x + 7)

= \frac{6 x ^{2} ( x + 7 )}{2 ( x + 6 ) ( x + 7 )}

Cancel the common factor:

x + 7

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

Factor the number:

6 = 2 \cdot 3

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

Cancel the common factor:

2

= \frac{3 x ^{2}}{x + 6}

(a + 2 x)^{7}

- 5 \times (- 6)

4 5^{2} + 9 0^{2}

\frac{9 - 10 i}{9 + i}

x^{4} - 13 x^{2} + 36

What is (6x^3+42x^2)/(2x^2+26x+84) ?
The solution to (6x^3+42x^2)/(2x^2+26x+84) is (3x^2)/(x+6)