# Solve for x 7/(x+7)+1=-x/(x+7)

Subtract from both sides of the equation.

Find the LCD of the terms in the equation.

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

The LCM is the smallest positive number that all of the numbers divide into evenly.

1. List the prime factors of each number.

2. Multiply each factor the greatest number of times it occurs in either number.

The number is not a prime number because it only has one positive factor, which is itself.

Not prime

The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either number.

The factor for is itself.

occurs time.

The LCM of is the result of multiplying all factors the greatest number of times they occur in either term.

Multiply each term in by to eliminate the fractions.

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Multiply each term in by .

Simplify the left side.

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Cancel the common factor of .

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Cancel the common factor.

Rewrite the expression.

Simplify the right side.

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Simplify each term.

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Cancel the common factor of .

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Move the leading negative in into the numerator.

Cancel the common factor.

Rewrite the expression.

Apply the distributive property.

Multiply by .

Subtract from .

Solve the equation.

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Rewrite the equation as .

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

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Add to both sides of the equation.

Add and .

Divide each term in by and simplify.

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Divide each term in by .

Simplify the left side.

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Cancel the common factor of .

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Cancel the common factor.

Divide by .

Simplify the right side.

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Divide by .

Exclude the solutions that do not make true.

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