Algebra Examples

$4 x^{3} {(x + 1)}^{- \frac{3}{2}} - x {(x + 1)}^{- \frac{1}{2}}$

Step 1

Factor $x$ out of $4 x^{3} {(x + 1)}^{- \frac{3}{2}} - x {(x + 1)}^{- \frac{1}{2}}$ .

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Step 1.1

Factor $x$ out of $4 x^{3} {(x + 1)}^{- \frac{3}{2}}$ .

$x (4 x^{2} {(x + 1)}^{- \frac{3}{2}}) - x {(x + 1)}^{- \frac{1}{2}}$

Step 1.2

Factor $x$ out of $- x {(x + 1)}^{- \frac{1}{2}}$ .

$x (4 x^{2} {(x + 1)}^{- \frac{3}{2}}) + x (- 1 {(x + 1)}^{- \frac{1}{2}})$

Step 1.3

Factor $x$ out of $x (4 x^{2} {(x + 1)}^{- \frac{3}{2}}) + x (- 1 {(x + 1)}^{- \frac{1}{2}})$ .

$x (4 x^{2} {(x + 1)}^{- \frac{3}{2}} - 1 {(x + 1)}^{- \frac{1}{2}})$

Step 2

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

$x (4 x^{2} \frac{1}{{(x + 1)}^{\frac{3}{2}}} - 1 {(x + 1)}^{- \frac{1}{2}})$

Step 3

Multiply $4 x^{2} \frac{1}{{(x + 1)}^{\frac{3}{2}}}$ .

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Step 3.1

Combine $4$ and $\frac{1}{{(x + 1)}^{\frac{3}{2}}}$ .

$x (x^{2} \frac{4}{{(x + 1)}^{\frac{3}{2}}} - 1 {(x + 1)}^{- \frac{1}{2}})$

Step 3.2

Combine $x^{2}$ and $\frac{4}{{(x + 1)}^{\frac{3}{2}}}$ .

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

Step 4

Move $4$ to the left of $x^{2}$ .

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

Step 5

Multiply $4$ by $x^{2}$ .

$x (\frac{4 x^{2}}{{(x + 1)}^{\frac{3}{2}}} - 1 {(x + 1)}^{- \frac{1}{2}})$

Step 6

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

$x (\frac{4 x^{2}}{{(x + 1)}^{\frac{3}{2}}} - 1 \frac{1}{{(x + 1)}^{\frac{1}{2}}})$

Step 7

Rewrite $- 1 \frac{1}{{(x + 1)}^{\frac{1}{2}}}$ as $- \frac{1}{{(x + 1)}^{\frac{1}{2}}}$ .

$x (\frac{4 x^{2}}{{(x + 1)}^{\frac{3}{2}}} - \frac{1}{{(x + 1)}^{\frac{1}{2}}})$