Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

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

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

Step 1.5

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

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

Step 1.6

Cancel the common factors.

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Step 1.6.1

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

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

Step 1.6.2

Factor $5$ out of $10$ .

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

Step 1.6.3

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

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

Step 1.6.4

Cancel the common factor.

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

Step 1.6.5

Rewrite the expression.

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

Step 2

Simplify the numerator.

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Step 2.1

Multiply $3$ by $5$ .

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

Step 2.2

Add $15$ and $1$ .

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

Step 3

Simplify the denominator.

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Step 3.1

Multiply $4$ by $- 1$ .

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

Step 3.2

Add $- 4$ and $2$ .

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

Step 4

Simplify the expression.

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Step 4.1

Multiply $- 1$ by $16$ .

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

Step 4.2

Divide $- 16$ by $- 2$ .

$8$