Evaluate ((3-4)^2-4|5-10|)/(151-3*5^2)

$\frac{{(3 - 4)}^{2} - 4 | 5 - 10 |}{151 - 3 \cdot 5^{2}}$

Step 1

Simplify the numerator.

Subtract $4$ from $3$ .

$\frac{{(- 1)}^{2} - 4 | 5 - 10 |}{151 - 3 \cdot 5^{2}}$

Raise $- 1$ to the power of $2$ .

$\frac{1 - 4 | 5 - 10 |}{151 - 3 \cdot 5^{2}}$

Subtract $10$ from $5$ .

$\frac{1 - 4 | - 5 |}{151 - 3 \cdot 5^{2}}$

The absolute value is the distance between a number and zero. The distance between $- 5$ and $0$ is $5$ .

$\frac{1 - 4 \cdot 5}{151 - 3 \cdot 5^{2}}$

Multiply $- 4$ by $5$ .

$\frac{1 - 20}{151 - 3 \cdot 5^{2}}$

Subtract $20$ from $1$ .

$\frac{- 19}{151 - 3 \cdot 5^{2}}$

Step 2

Simplify the denominator.

Raise $5$ to the power of $2$ .

$\frac{- 19}{151 - 3 \cdot 25}$

Multiply $- 3$ by $25$ .

$\frac{- 19}{151 - 75}$

Subtract $75$ from $151$ .

$\frac{- 19}{76}$

Step 3

Reduce the expression by cancelling the common factors.

Cancel the common factor of $- 19$ and $76$ .

Factor $19$ out of $- 19$ .

$\frac{19 (- 1)}{76}$

Cancel the common factors.

Factor $19$ out of $76$ .

$\frac{19 \cdot - 1}{19 \cdot 4}$

Cancel the common factor.

$\frac{19 \cdot - 1}{19 \cdot 4}$

Rewrite the expression.

$\frac{- 1}{4}$

Move the negative in front of the fraction.

$- \frac{1}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{4}$

Decimal Form:

$- 0.25$