Pre-Algebra Examples

$\frac{9 x - 17}{15 x - 30} \div \frac{6 x^{2 - 18}}{14 - 7}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{9 x - 17}{15 x - 30} \cdot \frac{14 - 7}{6 x^{2 - 18}}$

Step 2

Simplify with factoring out.

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Step 2.1

Factor $15$ out of $15 x - 30$ .

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Step 2.1.1

Factor $15$ out of $15 x$ .

$\frac{9 x - 17}{15 (x) - 30} \cdot \frac{14 - 7}{6 x^{2 - 18}}$

Step 2.1.2

Factor $15$ out of $- 30$ .

$\frac{9 x - 17}{15 x + 15 \cdot - 2} \cdot \frac{14 - 7}{6 x^{2 - 18}}$

Step 2.1.3

Factor $15$ out of $15 x + 15 \cdot - 2$ .

$\frac{9 x - 17}{15 (x - 2)} \cdot \frac{14 - 7}{6 x^{2 - 18}}$

Step 2.2

Move $x^{2 - 18}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{9 x - 17}{15 (x - 2)} \cdot \frac{(14 - 7) x^{- (2 - 18)}}{6}$

Step 3

Simplify the numerator.

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Step 3.1

Subtract $7$ from $14$ .

$\frac{9 x - 17}{15 (x - 2)} \cdot \frac{7 x^{- (2 - 18)}}{6}$

Step 3.2

Subtract $18$ from $2$ .

$\frac{9 x - 17}{15 (x - 2)} \cdot \frac{7 x^{- - 16}}{6}$

Step 3.3

Multiply $- 1$ by $- 16$ .

$\frac{9 x - 17}{15 (x - 2)} \cdot \frac{7 x^{16}}{6}$

Step 4

Multiply $\frac{9 x - 17}{15 (x - 2)} \cdot \frac{7 x^{16}}{6}$ .

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Step 4.1

Multiply $\frac{9 x - 17}{15 (x - 2)}$ by $\frac{7 x^{16}}{6}$ .

$\frac{(9 x - 17) (7 x^{16})}{15 (x - 2) \cdot 6}$

Step 4.2

Multiply $6$ by $15$ .

$\frac{(9 x - 17) (7 x^{16})}{90 (x - 2)}$

Step 5

Move $7$ to the left of $9 x - 17$ .

$\frac{7 \cdot (9 x - 17) x^{16}}{90 (x - 2)}$

Step 6

Reorder factors in $\frac{7 (9 x - 17) x^{16}}{90 (x - 2)}$ .

$\frac{7 x^{16} (9 x - 17)}{90 (x - 2)}$