Simplify (6r^2-7r+2)/(2r-1)*4/(15r-10)

$\frac{6 r^{2} - 7 r + 2}{2 r - 1} \cdot \frac{4}{15 r - 10}$

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 $a \cdot c = 6 \cdot 2 = 12$ and whose sum is $b = - 7$ .

Factor $- 7$ out of $- 7 r$ .

$\frac{6 r^{2} - 7 (r) + 2}{2 r - 1} \cdot \frac{4}{15 r - 10}$

Rewrite $- 7$ as $- 3$ plus $- 4$

$\frac{6 r^{2} + (- 3 - 4) r + 2}{2 r - 1} \cdot \frac{4}{15 r - 10}$

Apply the distributive property.

$\frac{6 r^{2} - 3 r - 4 r + 2}{2 r - 1} \cdot \frac{4}{15 r - 10}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{(6 r^{2} - 3 r) - 4 r + 2}{2 r - 1} \cdot \frac{4}{15 r - 10}$

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

$\frac{3 r (2 r - 1) - 2 (2 r - 1)}{2 r - 1} \cdot \frac{4}{15 r - 10}$

Factor the polynomial by factoring out the greatest common factor, $2 r - 1$ .

$\frac{(2 r - 1) (3 r - 2)}{2 r - 1} \cdot \frac{4}{15 r - 10}$

Step 2

Factor $5$ out of $15 r - 10$ .

Factor $5$ out of $15 r$ .

$\frac{(2 r - 1) (3 r - 2)}{2 r - 1} \cdot \frac{4}{5 (3 r) - 10}$

Factor $5$ out of $- 10$ .

$\frac{(2 r - 1) (3 r - 2)}{2 r - 1} \cdot \frac{4}{5 (3 r) + 5 (- 2)}$

Factor $5$ out of $5 (3 r) + 5 (- 2)$ .

$\frac{(2 r - 1) (3 r - 2)}{2 r - 1} \cdot \frac{4}{5 (3 r - 2)}$

Step 3

Cancel the common factor of $3 r - 2$ .

Factor $3 r - 2$ out of $(2 r - 1) (3 r - 2)$ .

$\frac{(3 r - 2) (2 r - 1)}{2 r - 1} \cdot \frac{4}{5 (3 r - 2)}$

Factor $3 r - 2$ out of $5 (3 r - 2)$ .

$\frac{(3 r - 2) (2 r - 1)}{2 r - 1} \cdot \frac{4}{(3 r - 2) \cdot 5}$

Cancel the common factor.

$\frac{(3 r - 2) (2 r - 1)}{2 r - 1} \cdot \frac{4}{(3 r - 2) \cdot 5}$

Rewrite the expression.

$\frac{2 r - 1}{2 r - 1} \cdot \frac{4}{5}$

Step 4

Multiply $\frac{2 r - 1}{2 r - 1}$ by $\frac{4}{5}$ .

$\frac{(2 r - 1) \cdot 4}{(2 r - 1) \cdot 5}$

Step 5

Cancel the common factor of $2 r - 1$ .

Cancel the common factor.

$\frac{(2 r - 1) \cdot 4}{(2 r - 1) \cdot 5}$

Rewrite the expression.

$\frac{4}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{5}$

Decimal Form:

$0.8$

Simplify (6r^2-7r+2)/(2r-1)*4/(15r-10)

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