Calculus Examples

$\frac{2 X - 7}{X + 1} = 1$

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 $\frac{2 X - 7}{X + 1} = 1$ by $X + 1$ to eliminate the fractions.

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Step 2.1

Multiply each term in $\frac{2 X - 7}{X + 1} = 1$ by $X + 1$ .

$\frac{2 X - 7}{X + 1} (X + 1) = 1 (X + 1)$

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.

$\frac{2 X - 7}{X + 1} (X + 1) = 1 (X + 1)$

Step 2.2.1.2

Rewrite the expression.

$2 X - 7 = 1 (X + 1)$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply $X + 1$ by $1$ .

$2 X - 7 = X + 1$

Step 3

Solve the equation.

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Step 3.1

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

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Step 3.1.1

Subtract $X$ from both sides of the equation.

$2 X - 7 - X = 1$

Step 3.1.2

Subtract $X$ from $2 X$ .

$X - 7 = 1$

Step 3.2

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

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Step 3.2.1

Add $7$ to both sides of the equation.

$X = 1 + 7$

Step 3.2.2

Add $1$ and $7$ .

$X = 8$