Finite Math Examples

$\frac{2.2}{\sqrt{x}} - 3.4 x^{- 2} + 8 x$

Step 1

Simplify each term.

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Step 1.1

Multiply $\frac{2.2}{\sqrt{x}}$ by $\frac{\sqrt{x}}{\sqrt{x}}$ .

$\frac{2.2}{\sqrt{x}} \cdot \frac{\sqrt{x}}{\sqrt{x}} - 3.4 x^{- 2} + 8 x$

Step 1.2

Combine and simplify the denominator.

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Step 1.2.1

Multiply $\frac{2.2}{\sqrt{x}}$ by $\frac{\sqrt{x}}{\sqrt{x}}$ .

$\frac{2.2 \sqrt{x}}{\sqrt{x} \sqrt{x}} - 3.4 x^{- 2} + 8 x$

Step 1.2.2

Raise $\sqrt{x}$ to the power of $1$ .

$\frac{2.2 \sqrt{x}}{{\sqrt{x}}^{1} \sqrt{x}} - 3.4 x^{- 2} + 8 x$

Step 1.2.3

Raise $\sqrt{x}$ to the power of $1$ .

$\frac{2.2 \sqrt{x}}{{\sqrt{x}}^{1} {\sqrt{x}}^{1}} - 3.4 x^{- 2} + 8 x$

Step 1.2.4

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

$\frac{2.2 \sqrt{x}}{{\sqrt{x}}^{1 + 1}} - 3.4 x^{- 2} + 8 x$

Step 1.2.5

Add $1$ and $1$ .

$\frac{2.2 \sqrt{x}}{{\sqrt{x}}^{2}} - 3.4 x^{- 2} + 8 x$

Step 1.2.6

Rewrite ${\sqrt{x}}^{2}$ as $x$ .

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Step 1.2.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x}$ as $x^{\frac{1}{2}}$ .

$\frac{2.2 \sqrt{x}}{{(x^{\frac{1}{2}})}^{2}} - 3.4 x^{- 2} + 8 x$

Step 1.2.6.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{2.2 \sqrt{x}}{x^{\frac{1}{2} \cdot 2}} - 3.4 x^{- 2} + 8 x$

Step 1.2.6.3

Combine $\frac{1}{2}$ and $2$ .

$\frac{2.2 \sqrt{x}}{x^{\frac{2}{2}}} - 3.4 x^{- 2} + 8 x$

Step 1.2.6.4

Cancel the common factor of $2$ .

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Step 1.2.6.4.1

Cancel the common factor.

$\frac{2.2 \sqrt{x}}{x^{\frac{2}{2}}} - 3.4 x^{- 2} + 8 x$

Step 1.2.6.4.2

Rewrite the expression.

$\frac{2.2 \sqrt{x}}{x^{1}} - 3.4 x^{- 2} + 8 x$

Step 1.2.6.5

Simplify.

$\frac{2.2 \sqrt{x}}{x} - 3.4 x^{- 2} + 8 x$

Step 1.3

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

$\frac{2.2 \sqrt{x}}{x} - 3.4 \frac{1}{x^{2}} + 8 x$

Step 1.4

Combine $- 3.4$ and $\frac{1}{x^{2}}$ .

$\frac{2.2 \sqrt{x}}{x} + \frac{- 3.4}{x^{2}} + 8 x$

Step 1.5

Move the negative in front of the fraction.

$\frac{2.2 \sqrt{x}}{x} - \frac{3.4}{x^{2}} + 8 x$

Step 2

To write $\frac{2.2 \sqrt{x}}{x}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{2.2 \sqrt{x}}{x} \cdot \frac{x}{x} - \frac{3.4}{x^{2}} + 8 x$

Step 3

Write each expression with a common denominator of $x^{2}$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{2.2 \sqrt{x}}{x}$ by $\frac{x}{x}$ .

$\frac{2.2 \sqrt{x} x}{x \cdot x} - \frac{3.4}{x^{2}} + 8 x$

Step 3.2

Multiply $x$ by $x$ .

$\frac{2.2 \sqrt{x} x}{x^{2}} - \frac{3.4}{x^{2}} + 8 x$

Step 4

Combine the numerators over the common denominator.

$\frac{2.2 \sqrt{x} x - 3.4}{x^{2}} + 8 x$

Step 5

Factor $0.2$ out of $2.2 \sqrt{x} x - 3.4$ .

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Step 5.1

Factor $0.2$ out of $2.2 \sqrt{x} x$ .

$\frac{0.2 (11 \sqrt{x} x) - 3.4}{x^{2}} + 8 x$

Step 5.2

Factor $0.2$ out of $- 3.4$ .

$\frac{0.2 (11 \sqrt{x} x) + 0.2 (- 17)}{x^{2}} + 8 x$

Step 5.3

Factor $0.2$ out of $0.2 (11 \sqrt{x} x) + 0.2 (- 17)$ .

$\frac{0.2 (11 \sqrt{x} x - 17)}{x^{2}} + 8 x$

Step 6

To write $8 x$ as a fraction with a common denominator, multiply by $\frac{x^{2}}{x^{2}}$ .

$\frac{0.2 (11 \sqrt{x} x - 17)}{x^{2}} + \frac{8 x \cdot x^{2}}{x^{2}}$

Step 7

Combine the numerators over the common denominator.

$\frac{0.2 (11 \sqrt{x} x - 17) + 8 x \cdot x^{2}}{x^{2}}$

Step 8

Simplify the numerator.

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Step 8.1

Factor $0.2$ out of $0.2 (11 \sqrt{x} x - 17) + 8 x \cdot x^{2}$ .

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Step 8.1.1

Factor $0.2$ out of $8 x \cdot x^{2}$ .

$\frac{0.2 (11 \sqrt{x} x - 17) + 0.2 (40 x \cdot x^{2})}{x^{2}}$

Step 8.1.2

Factor $0.2$ out of $0.2 (11 \sqrt{x} x - 17) + 0.2 (40 x \cdot x^{2})$ .

$\frac{0.2 (11 \sqrt{x} x - 17 + 40 x \cdot x^{2})}{x^{2}}$

Step 8.2

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

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Step 8.2.1

Move $x^{2}$ .

$\frac{0.2 (11 \sqrt{x} x - 17 + 40 (x^{2} x))}{x^{2}}$

Step 8.2.2

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

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Step 8.2.2.1

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

$\frac{0.2 (11 \sqrt{x} x - 17 + 40 (x^{2} x^{1}))}{x^{2}}$

Step 8.2.2.2

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

$\frac{0.2 (11 \sqrt{x} x - 17 + 40 x^{2 + 1})}{x^{2}}$

Step 8.2.3

Add $2$ and $1$ .

$\frac{0.2 (11 \sqrt{x} x - 17 + 40 x^{3})}{x^{2}}$