Algebra Examples

Solve in Terms of the Arbitrary Variable x
,
Step 1
Solve the equation for .
Step 1.1
Move all terms not containing to the right side of the equation.
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.
Step 1.2.1
Divide each term in by .
Step 1.2.2
Simplify the left side.
Step 1.2.2.1
Cancel the common factor of .
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.
Step 1.2.3.1
Simplify each term.
Step 1.2.3.1.1
Cancel the common factor of and .
Step 1.2.3.1.1.1
Factor out of .
Step 1.2.3.1.1.2
Cancel the common factors.
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 .
Step 2.1
Simplify .
Step 2.1.1
To write as a fraction with a common denominator, multiply by .
Step 2.1.2
Simplify terms.
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.
Step 2.1.3.1
Simplify the numerator.
Step 2.1.3.1.1
Factor out of .
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
Step 2.1.7.1
Reorder and .
Step 2.1.7.2
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.
Step 2.4.1
Simplify the left side.
Step 2.4.1.1
Cancel the common factor of .
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.
Step 2.4.2.1
Cancel the common factor of .
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.
Step 3.1
Simplify .
Step 3.1.1
Simplify each term.
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.
Step 3.1.1.3.1
Reduce the expression by cancelling the common factors.
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 .
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.
Step 3.1.5.1
Factor out of .
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.
Step 3.1.6.1
Cancel the common factor of and .
Step 3.1.6.1.1
Factor out of .
Step 3.1.6.1.2
Cancel the common factors.
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.
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.