Simplify (2a-7)/a*(3a^2)/(2a^2-11a+14)

$\frac{2 a - 7}{a} \cdot \frac{3 a^{2}}{2 a^{2} - 11 a + 14}$

Step 1

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 2 \cdot 14 = 28$ and whose sum is $b = - 11$ .

Factor $- 11$ out of $- 11 a$ .

$\frac{2 a - 7}{a} \cdot \frac{3 a^{2}}{2 a^{2} - 11 (a) + 14}$

Rewrite $- 11$ as $- 4$ plus $- 7$

$\frac{2 a - 7}{a} \cdot \frac{3 a^{2}}{2 a^{2} + (- 4 - 7) a + 14}$

Apply the distributive property.

$\frac{2 a - 7}{a} \cdot \frac{3 a^{2}}{2 a^{2} - 4 a - 7 a + 14}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{2 a - 7}{a} \cdot \frac{3 a^{2}}{(2 a^{2} - 4 a) - 7 a + 14}$

Factor out the greatest common factor (GCF) from each group.

$\frac{2 a - 7}{a} \cdot \frac{3 a^{2}}{2 a (a - 2) - 7 (a - 2)}$

Factor the polynomial by factoring out the greatest common factor, $a - 2$ .

$\frac{2 a - 7}{a} \cdot \frac{3 a^{2}}{(a - 2) (2 a - 7)}$

Step 2

Cancel the common factor of $2 a - 7$ .

Factor $2 a - 7$ out of $(a - 2) (2 a - 7)$ .

$\frac{2 a - 7}{a} \cdot \frac{3 a^{2}}{(2 a - 7) (a - 2)}$

Cancel the common factor.

$\frac{2 a - 7}{a} \cdot \frac{3 a^{2}}{(2 a - 7) (a - 2)}$

Rewrite the expression.

$\frac{1}{a} \cdot \frac{3 a^{2}}{a - 2}$

Step 3

Cancel the common factor of $a$ .

Factor $a$ out of $3 a^{2}$ .

$\frac{1}{a} \cdot \frac{a (3 a)}{a - 2}$

Cancel the common factor.

$\frac{1}{a} \cdot \frac{a (3 a)}{a - 2}$

Rewrite the expression.

$\frac{3 a}{a - 2}$

Simplify (2a-7)/a*(3a^2)/(2a^2-11a+14)

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