# Solve for t 1/45+1/90=1/t

Rewrite the equation as .

Factor each term.

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To write as a fraction with a common denominator, multiply by .

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

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Multiply and .

Multiply by .

Combine the numerators over the common denominator.

Add and .

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.

Since contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part then find LCM for the variable part .

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 prime factors for are .

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has factors of and .

has factors of and .

has factors of and .

The LCM of is .

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Multiply by .

Multiply by .

Multiply by .

The factor for is itself.

occurs time.

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

The LCM for is the numeric part multiplied by the variable part.

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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Rewrite using the commutative property of multiplication.

Combine and .

Cancel the common factor of .

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Cancel the common factor.

Rewrite the expression.

Simplify the right side.

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Cancel the common factor of .

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Factor out of .

Cancel the common factor.

Rewrite the expression.

Solve the equation.

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Rewrite the equation as .

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 .

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