Evaluate (3(-5^2)-5)/(4(-5)+10)

$\frac{3 (- 5^{2}) - 5}{4 (- 5) + 10}$

Step 1

Cancel the common factor of $3 (- 5^{2}) - 5$ and $4 (- 5) + 10$ .

Factor $- 1$ out of $3 (- 5^{2})$ .

$\frac{- (3 \cdot (5^{2})) - 5}{4 (- 5) + 10}$

Rewrite $- 5$ as $- 1 (5)$ .

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

Factor $- 1$ out of $- (3 \cdot (5^{2})) - 1 (5)$ .

$\frac{- (3 \cdot (5^{2}) + 5)}{4 (- 5) + 10}$

Rewrite $- (3 \cdot (5^{2}) + 5)$ as $- 1 (3 \cdot (5^{2}) + 5)$ .

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

Factor $5$ out of $- 1 (3 \cdot 5^{2} + 5)$ .

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

Cancel the common factors.

Factor $5$ out of $4 (- 5)$ .

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

Factor $5$ out of $10$ .

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

Factor $5$ out of $5 (4 \cdot (- 1)) + 5 (2)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

Simplify the numerator.

Multiply $3$ by $5$ .

$\frac{- 1 (15 + 1)}{4 \cdot (- 1) + 2}$

Add $15$ and $1$ .

$\frac{- 1 \cdot 16}{4 \cdot (- 1) + 2}$

Step 3

Simplify the denominator.

Multiply $4$ by $- 1$ .

$\frac{- 1 \cdot 16}{- 4 + 2}$

Add $- 4$ and $2$ .

$\frac{- 1 \cdot 16}{- 2}$

Step 4

Simplify the expression.

Multiply $- 1$ by $16$ .

$\frac{- 16}{- 2}$

Divide $- 16$ by $- 2$ .

$8$