Algebra Examples

$- 6 x {(- x + 7)}^{- \frac{4}{5}} - 7 {(- x + 7)}^{\frac{1}{5}}$

Step 1

Factor $- 1$ out of $- 6 x {(- x + 7)}^{- \frac{4}{5}} - 7 {(- x + 7)}^{\frac{1}{5}}$ .

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Step 1.1

Factor $- 1$ out of $- 6 x {(- x + 7)}^{- \frac{4}{5}}$ .

$- (6 x {(- x + 7)}^{- \frac{4}{5}}) - 7 {(- x + 7)}^{\frac{1}{5}}$

Step 1.2

Factor $- 1$ out of $- 7 {(- x + 7)}^{\frac{1}{5}}$ .

$- (6 x {(- x + 7)}^{- \frac{4}{5}}) - (7 {(- x + 7)}^{\frac{1}{5}})$

Step 1.3

Factor $- 1$ out of $- (6 x {(- x + 7)}^{- \frac{4}{5}}) - (7 {(- x + 7)}^{\frac{1}{5}})$ .

$- (6 x {(- x + 7)}^{- \frac{4}{5}} + 7 {(- x + 7)}^{\frac{1}{5}})$

Step 2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$- (6 x \frac{1}{{(- x + 7)}^{\frac{4}{5}}} + 7 {(- x + 7)}^{\frac{1}{5}})$

Step 3

Multiply $6 x \frac{1}{{(- x + 7)}^{\frac{4}{5}}}$ .

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Step 3.1

Combine $6$ and $\frac{1}{{(- x + 7)}^{\frac{4}{5}}}$ .

$- (x \frac{6}{{(- x + 7)}^{\frac{4}{5}}} + 7 {(- x + 7)}^{\frac{1}{5}})$

Step 3.2

Combine $x$ and $\frac{6}{{(- x + 7)}^{\frac{4}{5}}}$ .

$- (\frac{x \cdot 6}{{(- x + 7)}^{\frac{4}{5}}} + 7 {(- x + 7)}^{\frac{1}{5}})$

Step 4

Move $6$ to the left of $x$ .

$- (\frac{6 \cdot x}{{(- x + 7)}^{\frac{4}{5}}} + 7 {(- x + 7)}^{\frac{1}{5}})$

Step 5

Multiply $6$ by $x$ .

$- (\frac{6 x}{{(- x + 7)}^{\frac{4}{5}}} + 7 {(- x + 7)}^{\frac{1}{5}})$

Step 6

To write $7 {(- x + 7)}^{\frac{1}{5}}$ as a fraction with a common denominator, multiply by $\frac{{(- x + 7)}^{\frac{4}{5}}}{{(- x + 7)}^{\frac{4}{5}}}$ .

$- (\frac{6 x}{{(- x + 7)}^{\frac{4}{5}}} + \frac{7 {(- x + 7)}^{\frac{1}{5}} {(- x + 7)}^{\frac{4}{5}}}{{(- x + 7)}^{\frac{4}{5}}})$

Step 7

Combine the numerators over the common denominator.

$- \frac{6 x + 7 {(- x + 7)}^{\frac{1}{5}} {(- x + 7)}^{\frac{4}{5}}}{{(- x + 7)}^{\frac{4}{5}}}$

Step 8

Reorder terms.

$- \frac{7 {(- x + 7)}^{\frac{4}{5}} {(- x + 7)}^{\frac{1}{5}} + 6 x}{{(- x + 7)}^{\frac{4}{5}}}$

Step 9

Rewrite $\frac{7 {(- x + 7)}^{\frac{4}{5}} {(- x + 7)}^{\frac{1}{5}} + 6 x}{{(- x + 7)}^{\frac{4}{5}}}$ in a factored form.

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Step 9.1

Multiply ${(- x + 7)}^{\frac{4}{5}}$ by ${(- x + 7)}^{\frac{1}{5}}$ by adding the exponents.

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Step 9.1.1

Move ${(- x + 7)}^{\frac{1}{5}}$ .

$- \frac{7 ({(- x + 7)}^{\frac{1}{5}} {(- x + 7)}^{\frac{4}{5}}) + 6 x}{{(- x + 7)}^{\frac{4}{5}}}$

Step 9.1.2

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

$- \frac{7 {(- x + 7)}^{\frac{1}{5} + \frac{4}{5}} + 6 x}{{(- x + 7)}^{\frac{4}{5}}}$

Step 9.1.3

Combine the numerators over the common denominator.

$- \frac{7 {(- x + 7)}^{\frac{1 + 4}{5}} + 6 x}{{(- x + 7)}^{\frac{4}{5}}}$

Step 9.1.4

Add $1$ and $4$ .

$- \frac{7 {(- x + 7)}^{\frac{5}{5}} + 6 x}{{(- x + 7)}^{\frac{4}{5}}}$

Step 9.1.5

Divide $5$ by $5$ .

$- \frac{7 {(- x + 7)}^{1} + 6 x}{{(- x + 7)}^{\frac{4}{5}}}$

Step 9.2

Simplify $7 {(- x + 7)}^{1}$ .

$- \frac{7 (- x + 7) + 6 x}{{(- x + 7)}^{\frac{4}{5}}}$

Step 9.3

Apply the distributive property.

$- \frac{7 (- x) + 7 \cdot 7 + 6 x}{{(- x + 7)}^{\frac{4}{5}}}$

Step 9.4

Multiply $- 1$ by $7$ .

$- \frac{- 7 x + 7 \cdot 7 + 6 x}{{(- x + 7)}^{\frac{4}{5}}}$

Step 9.5

Multiply $7$ by $7$ .

$- \frac{- 7 x + 49 + 6 x}{{(- x + 7)}^{\frac{4}{5}}}$

Step 9.6

Add $- 7 x$ and $6 x$ .

$- \frac{- x + 49}{{(- x + 7)}^{\frac{4}{5}}}$

Step 10

Factor $- 1$ out of $- x + 49$ .

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Step 10.1

Factor $- 1$ out of $- x$ .

$- \frac{- (x) + 49}{{(- x + 7)}^{\frac{4}{5}}}$

Step 10.2

Rewrite $49$ as $- 1 (- 49)$ .

$- \frac{- (x) - 1 (- 49)}{{(- x + 7)}^{\frac{4}{5}}}$

Step 10.3

Factor $- 1$ out of $- (x) - 1 (- 49)$ .

$- \frac{- (x - 49)}{{(- x + 7)}^{\frac{4}{5}}}$