Algebra Examples

$\frac{3}{x} + 2 = \frac{5}{4 x} + \frac{17}{8}$

Step 1

Move all the expressions to the left side of the equation.

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Step 1.1

Subtract $\frac{5}{4 x}$ from both sides of the equation.

$\frac{3}{x} + 2 - \frac{5}{4 x} = \frac{17}{8}$

Step 1.2

Subtract $\frac{17}{8}$ from both sides of the equation.

$\frac{3}{x} + 2 - \frac{5}{4 x} - \frac{17}{8} = 0$

Step 2

Simplify $\frac{3}{x} + 2 - \frac{5}{4 x} - \frac{17}{8}$ .

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Step 2.1

To write $\frac{3}{x}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{3}{x} \cdot \frac{4}{4} - \frac{5}{4 x} + 2 - \frac{17}{8} = 0$

Step 2.2

Write each expression with a common denominator of $x \cdot 4$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.2.1

Multiply $\frac{3}{x}$ by $\frac{4}{4}$ .

$\frac{3 \cdot 4}{x \cdot 4} - \frac{5}{4 x} + 2 - \frac{17}{8} = 0$

Step 2.2.2

Move $4$ to the left of $x$ .

$\frac{3 \cdot 4}{4 x} - \frac{5}{4 x} + 2 - \frac{17}{8} = 0$

Step 2.3

Combine the numerators over the common denominator.

$\frac{3 \cdot 4 - 5}{4 x} + 2 - \frac{17}{8} = 0$

Step 2.4

Simplify the numerator.

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Step 2.4.1

Multiply $3$ by $4$ .

$\frac{12 - 5}{4 x} + 2 - \frac{17}{8} = 0$

Step 2.4.2

Subtract $5$ from $12$ .

$\frac{7}{4 x} + 2 - \frac{17}{8} = 0$

Step 2.5

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

$\frac{7}{4 x} + 2 \cdot \frac{8}{8} - \frac{17}{8} = 0$

Step 2.6

Combine $2$ and $\frac{8}{8}$ .

$\frac{7}{4 x} + \frac{2 \cdot 8}{8} - \frac{17}{8} = 0$

Step 2.7

Combine the numerators over the common denominator.

$\frac{7}{4 x} + \frac{2 \cdot 8 - 17}{8} = 0$

Step 2.8

Simplify the numerator.

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Step 2.8.1

Multiply $2$ by $8$ .

$\frac{7}{4 x} + \frac{16 - 17}{8} = 0$

Step 2.8.2

Subtract $17$ from $16$ .

$\frac{7}{4 x} + \frac{- 1}{8} = 0$

Step 2.9

Move the negative in front of the fraction.

$\frac{7}{4 x} - \frac{1}{8} = 0$

Step 3

Set the denominator in $\frac{7}{4 x}$ equal to $0$ to find where the expression is undefined.

$4 x = 0$

Step 4

Divide each term in $4 x = 0$ by $4$ and simplify.

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Step 4.1

Divide each term in $4 x = 0$ by $4$ .

$\frac{4 x}{4} = \frac{0}{4}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $4$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{0}{4}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{0}{4}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $0$ by $4$ .

$x = 0$

Step 5