Finite Math Examples

$\frac{8}{3 - 4 x} = \frac{5}{2 x + \frac{1}{4}}$

Step 1

Simplify both sides.

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Step 1.1

Simplify the denominator.

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Step 1.1.1

To write $2 x$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{8}{3 - 4 x} = \frac{5}{2 x \cdot \frac{4}{4} + \frac{1}{4}}$

Step 1.1.2

Combine $2 x$ and $\frac{4}{4}$ .

$\frac{8}{3 - 4 x} = \frac{5}{\frac{2 x \cdot 4}{4} + \frac{1}{4}}$

Step 1.1.3

Combine the numerators over the common denominator.

$\frac{8}{3 - 4 x} = \frac{5}{\frac{2 x \cdot 4 + 1}{4}}$

Step 1.1.4

Multiply $4$ by $2$ .

$\frac{8}{3 - 4 x} = \frac{5}{\frac{8 x + 1}{4}}$

Step 1.2

Multiply the numerator by the reciprocal of the denominator.

$\frac{8}{3 - 4 x} = 5 \frac{4}{8 x + 1}$

Step 1.3

Multiply $5 \frac{4}{8 x + 1}$ .

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Step 1.3.1

Combine $5$ and $\frac{4}{8 x + 1}$ .

$\frac{8}{3 - 4 x} = \frac{5 \cdot 4}{8 x + 1}$

Step 1.3.2

Multiply $5$ by $4$ .

$\frac{8}{3 - 4 x} = \frac{20}{8 x + 1}$

Step 2

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

$8 (8 x + 1) = (3 - 4 x) \cdot 20$

Step 3

Solve the equation for $x$ .

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Step 3.1

Simplify $8 (8 x + 1)$ .

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Step 3.1.1

Rewrite.

$0 + 0 + 8 (8 x + 1) = (3 - 4 x) \cdot 20$

Step 3.1.2

Simplify by adding zeros.

$8 (8 x + 1) = (3 - 4 x) \cdot 20$

Step 3.1.3

Apply the distributive property.

$8 (8 x) + 8 \cdot 1 = (3 - 4 x) \cdot 20$

Step 3.1.4

Multiply.

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Step 3.1.4.1

Multiply $8$ by $8$ .

$64 x + 8 \cdot 1 = (3 - 4 x) \cdot 20$

Step 3.1.4.2

Multiply $8$ by $1$ .

$64 x + 8 = (3 - 4 x) \cdot 20$

Step 3.2

Simplify $(3 - 4 x) \cdot 20$ .

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Step 3.2.1

Apply the distributive property.

$64 x + 8 = 3 \cdot 20 - 4 x \cdot 20$

Step 3.2.2

Multiply.

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Step 3.2.2.1

Multiply $3$ by $20$ .

$64 x + 8 = 60 - 4 x \cdot 20$

Step 3.2.2.2

Multiply $20$ by $- 4$ .

$64 x + 8 = 60 - 80 x$

Step 3.3

Move all terms containing $x$ to the left side of the equation.

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Step 3.3.1

Add $80 x$ to both sides of the equation.

$64 x + 8 + 80 x = 60$

Step 3.3.2

Add $64 x$ and $80 x$ .

$144 x + 8 = 60$

Step 3.4

Move all terms not containing $x$ to the right side of the equation.

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Step 3.4.1

Subtract $8$ from both sides of the equation.

$144 x = 60 - 8$

Step 3.4.2

Subtract $8$ from $60$ .

$144 x = 52$

Step 3.5

Divide each term in $144 x = 52$ by $144$ and simplify.

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Step 3.5.1

Divide each term in $144 x = 52$ by $144$ .

$\frac{144 x}{144} = \frac{52}{144}$

Step 3.5.2

Simplify the left side.

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Step 3.5.2.1

Cancel the common factor of $144$ .

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Step 3.5.2.1.1

Cancel the common factor.

$\frac{144 x}{144} = \frac{52}{144}$

Step 3.5.2.1.2

Divide $x$ by $1$ .

$x = \frac{52}{144}$

Step 3.5.3

Simplify the right side.

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Step 3.5.3.1

Cancel the common factor of $52$ and $144$ .

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Step 3.5.3.1.1

Factor $4$ out of $52$ .

$x = \frac{4 (13)}{144}$

Step 3.5.3.1.2

Cancel the common factors.

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Step 3.5.3.1.2.1

Factor $4$ out of $144$ .

$x = \frac{4 \cdot 13}{4 \cdot 36}$

Step 3.5.3.1.2.2

Cancel the common factor.

$x = \frac{4 \cdot 13}{4 \cdot 36}$

Step 3.5.3.1.2.3

Rewrite the expression.

$x = \frac{13}{36}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{13}{36}$

Decimal Form:

$x = 0.36\overline{1}$