Algebra Examples

Solve in Terms of the Arbitrary Variable x
,
Step 1
Solve the equation for .
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Step 1.1
Move all terms not containing to the right side of the equation.
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Step 1.1.1
Add to both sides of the equation.
Step 1.1.2
Subtract from both sides of the equation.
Step 1.2
Divide each term in by and simplify.
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Step 1.2.1
Divide each term in by .
Step 1.2.2
Simplify the left side.
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Step 1.2.2.1
Cancel the common factor of .
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Step 1.2.2.1.1
Cancel the common factor.
Step 1.2.2.1.2
Divide by .
Step 1.2.3
Simplify the right side.
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Step 1.2.3.1
Simplify each term.
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Step 1.2.3.1.1
Cancel the common factor of and .
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Step 1.2.3.1.1.1
Factor out of .
Step 1.2.3.1.1.2
Cancel the common factors.
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Step 1.2.3.1.1.2.1
Factor out of .
Step 1.2.3.1.1.2.2
Cancel the common factor.
Step 1.2.3.1.1.2.3
Rewrite the expression.
Step 1.2.3.1.2
Move the negative in front of the fraction.
Step 2
Solve the equation for .
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Step 2.1
Simplify .
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Step 2.1.1
To write as a fraction with a common denominator, multiply by .
Step 2.1.2
Simplify terms.
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Step 2.1.2.1
Combine and .
Step 2.1.2.2
Combine the numerators over the common denominator.
Step 2.1.3
Simplify each term.
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Step 2.1.3.1
Simplify the numerator.
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Step 2.1.3.1.1
Factor out of .
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Step 2.1.3.1.1.1
Raise to the power of .
Step 2.1.3.1.1.2
Factor out of .
Step 2.1.3.1.1.3
Factor out of .
Step 2.1.3.1.1.4
Factor out of .
Step 2.1.3.1.2
Multiply by .
Step 2.1.3.1.3
Subtract from .
Step 2.1.3.2
Move to the left of .
Step 2.1.3.3
Move the negative in front of the fraction.
Step 2.1.4
To write as a fraction with a common denominator, multiply by .
Step 2.1.5
Combine and .
Step 2.1.6
Combine the numerators over the common denominator.
Step 2.1.7
Add and .
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Step 2.1.7.1
Reorder and .
Step 2.1.7.2
Add and .
Step 2.2
Add to both sides of the equation.
Step 2.3
Multiply both sides of the equation by .
Step 2.4
Simplify both sides of the equation.
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Step 2.4.1
Simplify the left side.
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Step 2.4.1.1
Cancel the common factor of .
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Step 2.4.1.1.1
Cancel the common factor.
Step 2.4.1.1.2
Rewrite the expression.
Step 2.4.2
Simplify the right side.
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Step 2.4.2.1
Cancel the common factor of .
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Step 2.4.2.1.1
Factor out of .
Step 2.4.2.1.2
Cancel the common factor.
Step 2.4.2.1.3
Rewrite the expression.
Step 3
Simplify the right side.
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Step 3.1
Simplify .
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Step 3.1.1
Simplify each term.
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Step 3.1.1.1
Combine and .
Step 3.1.1.2
Multiply by .
Step 3.1.1.3
Reduce the expression by cancelling the common factors.
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Step 3.1.1.3.1
Reduce the expression by cancelling the common factors.
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Step 3.1.1.3.1.1
Factor out of .
Step 3.1.1.3.1.2
Factor out of .
Step 3.1.1.3.1.3
Cancel the common factor.
Step 3.1.1.3.1.4
Rewrite the expression.
Step 3.1.1.3.2
Divide by .
Step 3.1.2
To write as a fraction with a common denominator, multiply by .
Step 3.1.3
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 3.1.3.1
Multiply by .
Step 3.1.3.2
Multiply by .
Step 3.1.4
Combine the numerators over the common denominator.
Step 3.1.5
Simplify the numerator.
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Step 3.1.5.1
Factor out of .
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Step 3.1.5.1.1
Raise to the power of .
Step 3.1.5.1.2
Factor out of .
Step 3.1.5.1.3
Factor out of .
Step 3.1.5.1.4
Factor out of .
Step 3.1.5.2
Multiply by .
Step 3.1.5.3
Subtract from .
Step 3.1.6
Reduce the expression by cancelling the common factors.
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Step 3.1.6.1
Cancel the common factor of and .
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Step 3.1.6.1.1
Factor out of .
Step 3.1.6.1.2
Cancel the common factors.
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Step 3.1.6.1.2.1
Factor out of .
Step 3.1.6.1.2.2
Cancel the common factor.
Step 3.1.6.1.2.3
Rewrite the expression.
Step 3.1.6.2
Simplify the expression.
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Step 3.1.6.2.1
Move to the left of .
Step 3.1.6.2.2
Move the negative in front of the fraction.
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