What is (k+3)/(4k-2)*(12k^2+2k-4) ?

The solution to (k+3)/(4k-2)*(12k^2+2k-4) is (k+3)(3k+2)

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simplify (k+3)/(4k-2)*(12k^2+2k-4)

simplify

\frac{k + 3}{4 k - 2} \cdot (12 k^{2} + 2 k - 4)

(k + 3) (3 k + 2)

Solution steps

\frac{k + 3}{4 k - 2} (12 k^{2} + 2 k - 4)

Apply the fraction rule:

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

= \frac{( k + 3 ) ( 12 k ^{2} + 2 k - 4 )}{4 k - 2}

Factor

12 k^{2} + 2 k - 4 : 2 (2 k - 1) (3 k + 2)

= \frac{( k + 3 ) \cdot 2 ( 2 k - 1 ) ( 3 k + 2 )}{4 k - 2}

Factor

4 k - 2 : 2 (2 k - 1)

= \frac{( k + 3 ) \cdot 2 ( 2 k - 1 ) ( 3 k + 2 )}{2 ( 2 k - 1 )}

Cancel the common factor:

2

= \frac{( k + 3 ) ( 2 k - 1 ) ( 3 k + 2 )}{2 k - 1}

Cancel the common factor:

2 k - 1

= (k + 3) (3 k + 2)

(x + 4) (2 x - 3)

2 sin (4 θ) cos (4 θ)

0.25 \cdot 4^{3} - 1

What is (k+3)/(4k-2)*(12k^2+2k-4) ?
The solution to (k+3)/(4k-2)*(12k^2+2k-4) is (k+3)(3k+2)