Precalculus Examples

$2 x^{2} {(x - 1)}^{0.5} - 5 {(x - 1)}^{- 0.5}$

Step 1

Simplify each term.

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Step 1.1

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

$2 x^{2} {(x - 1)}^{0.5} - 5 \frac{1}{{(x - 1)}^{0.5}}$

Step 1.2

Combine $- 5$ and $\frac{1}{{(x - 1)}^{0.5}}$ .

$2 x^{2} {(x - 1)}^{0.5} + \frac{- 5}{{(x - 1)}^{0.5}}$

Step 1.3

Move the negative in front of the fraction.

$2 x^{2} {(x - 1)}^{0.5} - \frac{5}{{(x - 1)}^{0.5}}$

Step 2

To write $2 x^{2} {(x - 1)}^{0.5}$ as a fraction with a common denominator, multiply by $\frac{{(x - 1)}^{0.5}}{{(x - 1)}^{0.5}}$ .

$\frac{2 x^{2} {(x - 1)}^{0.5} {(x - 1)}^{0.5}}{{(x - 1)}^{0.5}} - \frac{5}{{(x - 1)}^{0.5}}$

Step 3

Combine the numerators over the common denominator.

$\frac{2 x^{2} {(x - 1)}^{0.5} {(x - 1)}^{0.5} - 5}{{(x - 1)}^{0.5}}$

Step 4

Simplify the numerator.

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Step 4.1

Multiply ${(x - 1)}^{0.5}$ by ${(x - 1)}^{0.5}$ by adding the exponents.

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Step 4.1.1

Move ${(x - 1)}^{0.5}$ .

$\frac{2 x^{2} ({(x - 1)}^{0.5} {(x - 1)}^{0.5}) - 5}{{(x - 1)}^{0.5}}$

Step 4.1.2

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

$\frac{2 x^{2} {(x - 1)}^{0.5 + 0.5} - 5}{{(x - 1)}^{0.5}}$

Step 4.1.3

Add $0.5$ and $0.5$ .

$\frac{2 x^{2} {(x - 1)}^{1} - 5}{{(x - 1)}^{0.5}}$

Step 4.2

Simplify $2 x^{2} {(x - 1)}^{1}$ .

$\frac{2 x^{2} (x - 1) - 5}{{(x - 1)}^{0.5}}$

Step 4.3

Apply the distributive property.

$\frac{2 x^{2} x + 2 x^{2} \cdot - 1 - 5}{{(x - 1)}^{0.5}}$

Step 4.4

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 4.4.1

Move $x$ .

$\frac{2 (x \cdot x^{2}) + 2 x^{2} \cdot - 1 - 5}{{(x - 1)}^{0.5}}$

Step 4.4.2

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

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Step 4.4.2.1

Raise $x$ to the power of $1$ .

$\frac{2 (x^{1} x^{2}) + 2 x^{2} \cdot - 1 - 5}{{(x - 1)}^{0.5}}$

Step 4.4.2.2

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

$\frac{2 x^{1 + 2} + 2 x^{2} \cdot - 1 - 5}{{(x - 1)}^{0.5}}$

Step 4.4.3

Add $1$ and $2$ .

$\frac{2 x^{3} + 2 x^{2} \cdot - 1 - 5}{{(x - 1)}^{0.5}}$

Step 4.5

Multiply $- 1$ by $2$ .

$\frac{2 x^{3} - 2 x^{2} - 5}{{(x - 1)}^{0.5}}$