Algebra Examples

$\frac{4 x + 3}{x - 8} = \frac{7}{8 - x}$

Step 1

Subtract $\frac{7}{8 - x}$ from both sides of the equation.

$\frac{4 x + 3}{x - 8} - \frac{7}{8 - x} = 0$

Step 2

Simplify $\frac{4 x + 3}{x - 8} - \frac{7}{8 - x}$ .

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Step 2.1

Rewrite $8$ as $- 1 (- 8)$ .

$\frac{4 x + 3}{x - 8} - \frac{7}{- 1 (- 8) - x} = 0$

Step 2.2

Factor $- 1$ out of $- x$ .

$\frac{4 x + 3}{x - 8} - \frac{7}{- 1 (- 8) - (x)} = 0$

Step 2.3

Factor $- 1$ out of $- 1 (- 8) - (x)$ .

$\frac{4 x + 3}{x - 8} - \frac{7}{- 1 (- 8 + x)} = 0$

Step 2.4

Reorder terms.

$\frac{4 x + 3}{x - 8} - \frac{7}{- 1 (x - 8)} = 0$

Step 2.5

To write $\frac{4 x + 3}{x - 8}$ as a fraction with a common denominator, multiply by $\frac{- 1}{- 1}$ .

$\frac{4 x + 3}{x - 8} \cdot \frac{- 1}{- 1} - \frac{7}{- 1 (x - 8)} = 0$

Step 2.6

Write each expression with a common denominator of $(x - 8) \cdot - 1$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.6.1

Multiply $\frac{4 x + 3}{x - 8}$ by $\frac{- 1}{- 1}$ .

$\frac{(4 x + 3) \cdot - 1}{(x - 8) \cdot - 1} - \frac{7}{- 1 (x - 8)} = 0$

Step 2.6.2

Reorder the factors of $(x - 8) \cdot - 1$ .

$\frac{(4 x + 3) \cdot - 1}{- (x - 8)} - \frac{7}{- 1 (x - 8)} = 0$

Step 2.7

Combine the numerators over the common denominator.

$\frac{(4 x + 3) \cdot - 1 - 7}{- (x - 8)} = 0$

Step 2.8

Simplify the numerator.

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Step 2.8.1

Apply the distributive property.

$\frac{4 x \cdot - 1 + 3 \cdot - 1 - 7}{- (x - 8)} = 0$

Step 2.8.2

Multiply $- 1$ by $4$ .

$\frac{- 4 x + 3 \cdot - 1 - 7}{- (x - 8)} = 0$

Step 2.8.3

Multiply $3$ by $- 1$ .

$\frac{- 4 x - 3 - 7}{- (x - 8)} = 0$

Step 2.8.4

Subtract $7$ from $- 3$ .

$\frac{- 4 x - 10}{- (x - 8)} = 0$

Step 2.8.5

Factor $2$ out of $- 4 x - 10$ .

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Step 2.8.5.1

Factor $2$ out of $- 4 x$ .

$\frac{2 (- 2 x) - 10}{- (x - 8)} = 0$

Step 2.8.5.2

Factor $2$ out of $- 10$ .

$\frac{2 (- 2 x) + 2 (- 5)}{- (x - 8)} = 0$

Step 2.8.5.3

Factor $2$ out of $2 (- 2 x) + 2 (- 5)$ .

$\frac{2 (- 2 x - 5)}{- (x - 8)} = 0$

Step 2.9

Move the negative in front of the fraction.

$- \frac{2 (- 2 x - 5)}{x - 8} = 0$

Step 2.10

Factor $- 1$ out of $- 2 x$ .

$- \frac{2 (- (2 x) - 5)}{x - 8} = 0$

Step 2.11

Rewrite $- 5$ as $- 1 (5)$ .

$- \frac{2 (- (2 x) - 1 (5))}{x - 8} = 0$

Step 2.12

Factor $- 1$ out of $- (2 x) - 1 (5)$ .

$- \frac{2 (- (2 x + 5))}{x - 8} = 0$

Step 2.13

Rewrite $- (2 x + 5)$ as $- 1 (2 x + 5)$ .

$- \frac{2 (- 1 (2 x + 5))}{x - 8} = 0$

Step 2.14

Move the negative in front of the fraction.

$- - \frac{2 (2 x + 5)}{x - 8} = 0$

Step 2.15

Multiply $- 1$ by $- 1$ .

$1 \frac{2 (2 x + 5)}{x - 8} = 0$

Step 2.16

Multiply $\frac{2 (2 x + 5)}{x - 8}$ by $1$ .

$\frac{2 (2 x + 5)}{x - 8} = 0$

Step 3

Set the numerator equal to zero.

$2 (2 x + 5) = 0$

Step 4

Solve the equation for $x$ .

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Step 4.1

Divide each term in $2 (2 x + 5) = 0$ by $2$ and simplify.

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Step 4.1.1

Divide each term in $2 (2 x + 5) = 0$ by $2$ .

$\frac{2 (2 x + 5)}{2} = \frac{0}{2}$

Step 4.1.2

Simplify the left side.

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Step 4.1.2.1

Cancel the common factor of $2$ .

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Step 4.1.2.1.1

Cancel the common factor.

$\frac{2 (2 x + 5)}{2} = \frac{0}{2}$

Step 4.1.2.1.2

Divide $2 x + 5$ by $1$ .

$2 x + 5 = \frac{0}{2}$

Step 4.1.3

Simplify the right side.

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Step 4.1.3.1

Divide $0$ by $2$ .

$2 x + 5 = 0$

Step 4.2

Subtract $5$ from both sides of the equation.

$2 x = - 5$

Step 4.3

Divide each term in $2 x = - 5$ by $2$ and simplify.

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Step 4.3.1

Divide each term in $2 x = - 5$ by $2$ .

$\frac{2 x}{2} = \frac{- 5}{2}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $2$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 5}{2}$

Step 4.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 5}{2}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Move the negative in front of the fraction.

$x = - \frac{5}{2}$