Simplify (10/(5r-4))÷((r+5)/(5r^2-49r+36))

$\frac{10}{5 r - 4} \div \frac{r + 5}{5 r^{2} - 49 r + 36}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{10}{5 r - 4} \cdot \frac{5 r^{2} - 49 r + 36}{r + 5}$

Step 2

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 $a \cdot c = 5 \cdot 36 = 180$ and whose sum is $b = - 49$ .

Factor $- 49$ out of $- 49 r$ .

$\frac{10}{5 r - 4} \cdot \frac{5 r^{2} - 49 (r) + 36}{r + 5}$

Rewrite $- 49$ as $- 4$ plus $- 45$

$\frac{10}{5 r - 4} \cdot \frac{5 r^{2} + (- 4 - 45) r + 36}{r + 5}$

Apply the distributive property.

$\frac{10}{5 r - 4} \cdot \frac{5 r^{2} - 4 r - 45 r + 36}{r + 5}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{10}{5 r - 4} \cdot \frac{(5 r^{2} - 4 r) - 45 r + 36}{r + 5}$

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

$\frac{10}{5 r - 4} \cdot \frac{r (5 r - 4) - 9 (5 r - 4)}{r + 5}$

Factor the polynomial by factoring out the greatest common factor, $5 r - 4$ .

$\frac{10}{5 r - 4} \cdot \frac{(5 r - 4) (r - 9)}{r + 5}$

Step 3

Cancel the common factor of $5 r - 4$ .

Cancel the common factor.

$\frac{10}{5 r - 4} \cdot \frac{(5 r - 4) (r - 9)}{r + 5}$

Rewrite the expression.

$10 \frac{r - 9}{r + 5}$

Step 4

Combine $10$ and $\frac{r - 9}{r + 5}$ .

$\frac{10 (r - 9)}{r + 5}$

Simplify (10/(5r-4))÷((r+5)/(5r^2-49r+36))

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