Algebra Examples

Solve the Rational Equation for x (2x+6)/(x-5)=(x+3)/(x-1)
Step 1
Factor out of .
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Step 1.1
Factor out of .
Step 1.2
Factor out of .
Step 1.3
Factor out of .
Step 2
Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.
Step 3
Solve the equation for .
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Step 3.1
Simplify .
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Step 3.1.1
Rewrite.
Step 3.1.2
Simplify by multiplying through.
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Step 3.1.2.1
Apply the distributive property.
Step 3.1.2.2
Multiply by .
Step 3.1.3
Expand using the FOIL Method.
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Step 3.1.3.1
Apply the distributive property.
Step 3.1.3.2
Apply the distributive property.
Step 3.1.3.3
Apply the distributive property.
Step 3.1.4
Simplify and combine like terms.
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Step 3.1.4.1
Simplify each term.
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Step 3.1.4.1.1
Multiply by by adding the exponents.
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Step 3.1.4.1.1.1
Move .
Step 3.1.4.1.1.2
Multiply by .
Step 3.1.4.1.2
Multiply by .
Step 3.1.4.1.3
Multiply by .
Step 3.1.4.2
Add and .
Step 3.2
Simplify .
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Step 3.2.1
Expand using the FOIL Method.
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Step 3.2.1.1
Apply the distributive property.
Step 3.2.1.2
Apply the distributive property.
Step 3.2.1.3
Apply the distributive property.
Step 3.2.2
Simplify and combine like terms.
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Step 3.2.2.1
Simplify each term.
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Step 3.2.2.1.1
Multiply by .
Step 3.2.2.1.2
Move to the left of .
Step 3.2.2.1.3
Multiply by .
Step 3.2.2.2
Subtract from .
Step 3.3
Move all terms containing to the left side of the equation.
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Step 3.3.1
Subtract from both sides of the equation.
Step 3.3.2
Add to both sides of the equation.
Step 3.3.3
Subtract from .
Step 3.3.4
Add and .
Step 3.4
Add to both sides of the equation.
Step 3.5
Add and .
Step 3.6
Factor using the perfect square rule.
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Step 3.6.1
Rewrite as .
Step 3.6.2
Check that the middle term is two times the product of the numbers being squared in the first term and third term.
Step 3.6.3
Rewrite the polynomial.
Step 3.6.4
Factor using the perfect square trinomial rule , where and .
Step 3.7
Set the equal to .
Step 3.8
Subtract from both sides of the equation.