Finite Math Examples

$\frac{4 {(3 x - 4)}^{\frac{1}{7}} - (x - 4) {(3 x - 4)}^{\frac{- 6}{7}}}{{(3 x - 4)}^{\frac{6}{7}}}$

Step 1

Simplify the numerator.

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Step 1.1

Factor ${(3 x - 4)}^{\frac{- 6}{7}}$ out of $4 {(3 x - 4)}^{\frac{1}{7}} - (x - 4) {(3 x - 4)}^{\frac{- 6}{7}}$ .

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Step 1.1.1

Factor ${(3 x - 4)}^{\frac{- 6}{7}}$ out of $4 {(3 x - 4)}^{\frac{1}{7}}$ .

$\frac{{(3 x - 4)}^{\frac{- 6}{7}} (4 {(3 x - 4)}^{\frac{7}{7}}) - (x - 4) {(3 x - 4)}^{\frac{- 6}{7}}}{{(3 x - 4)}^{\frac{6}{7}}}$

Step 1.1.2

Factor ${(3 x - 4)}^{\frac{- 6}{7}}$ out of $- (x - 4) {(3 x - 4)}^{\frac{- 6}{7}}$ .

$\frac{{(3 x - 4)}^{\frac{- 6}{7}} (4 {(3 x - 4)}^{\frac{7}{7}}) + {(3 x - 4)}^{\frac{- 6}{7}} (- (x - 4))}{{(3 x - 4)}^{\frac{6}{7}}}$

Step 1.1.3

Factor ${(3 x - 4)}^{\frac{- 6}{7}}$ out of ${(3 x - 4)}^{\frac{- 6}{7}} (4 {(3 x - 4)}^{\frac{7}{7}}) + {(3 x - 4)}^{\frac{- 6}{7}} (- (x - 4))$ .

$\frac{{(3 x - 4)}^{\frac{- 6}{7}} (4 {(3 x - 4)}^{\frac{7}{7}} - (x - 4))}{{(3 x - 4)}^{\frac{6}{7}}}$

Step 1.2

Divide $7$ by $7$ .

$\frac{{(3 x - 4)}^{\frac{- 6}{7}} (4 {(3 x - 4)}^{1} - (x - 4))}{{(3 x - 4)}^{\frac{6}{7}}}$

Step 1.3

Simplify.

$\frac{{(3 x - 4)}^{\frac{- 6}{7}} (4 (3 x - 4) - (x - 4))}{{(3 x - 4)}^{\frac{6}{7}}}$

Step 1.4

Apply the distributive property.

$\frac{{(3 x - 4)}^{\frac{- 6}{7}} (4 (3 x) + 4 \cdot - 4 - (x - 4))}{{(3 x - 4)}^{\frac{6}{7}}}$

Step 1.5

Multiply $3$ by $4$ .

$\frac{{(3 x - 4)}^{\frac{- 6}{7}} (12 x + 4 \cdot - 4 - (x - 4))}{{(3 x - 4)}^{\frac{6}{7}}}$

Step 1.6

Multiply $4$ by $- 4$ .

$\frac{{(3 x - 4)}^{\frac{- 6}{7}} (12 x - 16 - (x - 4))}{{(3 x - 4)}^{\frac{6}{7}}}$

Step 1.7

Apply the distributive property.

$\frac{{(3 x - 4)}^{\frac{- 6}{7}} (12 x - 16 - x - - 4)}{{(3 x - 4)}^{\frac{6}{7}}}$

Step 1.8

Multiply $- 1$ by $- 4$ .

$\frac{{(3 x - 4)}^{\frac{- 6}{7}} (12 x - 16 - x + 4)}{{(3 x - 4)}^{\frac{6}{7}}}$

Step 1.9

Subtract $x$ from $12 x$ .

$\frac{{(3 x - 4)}^{\frac{- 6}{7}} (11 x - 16 + 4)}{{(3 x - 4)}^{\frac{6}{7}}}$

Step 1.10

Add $- 16$ and $4$ .

$\frac{{(3 x - 4)}^{\frac{- 6}{7}} (11 x - 12)}{{(3 x - 4)}^{\frac{6}{7}}}$

Step 2

Move ${(3 x - 4)}^{\frac{- 6}{7}}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{11 x - 12}{{(3 x - 4)}^{\frac{6}{7}} {(3 x - 4)}^{- \frac{- 6}{7}}}$

Step 3

Multiply ${(3 x - 4)}^{\frac{6}{7}}$ by ${(3 x - 4)}^{- \frac{- 6}{7}}$ by adding the exponents.

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Step 3.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{11 x - 12}{{(3 x - 4)}^{\frac{6}{7} - \frac{- 6}{7}}}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{11 x - 12}{{(3 x - 4)}^{\frac{6 + 6}{7}}}$

Step 3.3

Add $6$ and $6$ .

$\frac{11 x - 12}{{(3 x - 4)}^{\frac{12}{7}}}$