Algebra Examples

$\frac{5 x}{x + 1} = 4$

Step 1

Find the LCD of the terms in the equation.

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Step 1.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$x + 1, 1$

Step 1.2

Remove parentheses.

$x + 1, 1$

Step 1.3

The LCM of one and any expression is the expression.

$x + 1$

Step 2

Multiply each term in $\frac{5 x}{x + 1} = 4$ by $x + 1$ to eliminate the fractions.

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Step 2.1

Multiply each term in $\frac{5 x}{x + 1} = 4$ by $x + 1$ .

$\frac{5 x}{x + 1} (x + 1) = 4 (x + 1)$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $x + 1$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{5 x}{x + 1} (x + 1) = 4 (x + 1)$

Step 2.2.1.2

Rewrite the expression.

$5 x = 4 (x + 1)$

Step 2.3

Simplify the right side.

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Step 2.3.1

Apply the distributive property.

$5 x = 4 x + 4 \cdot 1$

Step 2.3.2

Multiply $4$ by $1$ .

$5 x = 4 x + 4$

Step 3

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

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Step 3.1

Subtract $4 x$ from both sides of the equation.

$5 x - 4 x = 4$

Step 3.2

Subtract $4 x$ from $5 x$ .

$x = 4$