Basic Math Examples

Solve for y (y-2)/5-(5-2y)/4=4-y-(4y-1)/20
Step 1
Simplify .
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Step 1.1
To write as a fraction with a common denominator, multiply by .
Step 1.2
To write as a fraction with a common denominator, multiply by .
Step 1.3
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 1.3.1
Multiply by .
Step 1.3.2
Multiply by .
Step 1.3.3
Multiply by .
Step 1.3.4
Multiply by .
Step 1.4
Combine the numerators over the common denominator.
Step 1.5
Simplify the numerator.
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Step 1.5.1
Apply the distributive property.
Step 1.5.2
Move to the left of .
Step 1.5.3
Multiply by .
Step 1.5.4
Apply the distributive property.
Step 1.5.5
Multiply by .
Step 1.5.6
Multiply by .
Step 1.5.7
Apply the distributive property.
Step 1.5.8
Multiply by .
Step 1.5.9
Multiply by .
Step 1.5.10
Add and .
Step 1.5.11
Subtract from .
Step 2
Simplify .
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Step 2.1
To write as a fraction with a common denominator, multiply by .
Step 2.2
Simplify terms.
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Step 2.2.1
Combine and .
Step 2.2.2
Combine the numerators over the common denominator.
Step 2.2.3
Multiply by .
Step 2.3
Simplify the numerator.
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Step 2.3.1
Apply the distributive property.
Step 2.3.2
Multiply by .
Step 2.3.3
Multiply by .
Step 2.3.4
Add and .
Step 2.4
To write as a fraction with a common denominator, multiply by .
Step 2.5
Simplify terms.
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Step 2.5.1
Combine and .
Step 2.5.2
Combine the numerators over the common denominator.
Step 2.6
Simplify the numerator.
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Step 2.6.1
Multiply by .
Step 2.6.2
Subtract from .
Step 2.6.3
Factor out of .
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Step 2.6.3.1
Factor out of .
Step 2.6.3.2
Factor out of .
Step 2.6.3.3
Factor out of .
Step 2.7
Simplify with factoring out.
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Step 2.7.1
Factor out of .
Step 2.7.2
Rewrite as .
Step 2.7.3
Factor out of .
Step 2.7.4
Simplify the expression.
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Step 2.7.4.1
Rewrite as .
Step 2.7.4.2
Move the negative in front of the fraction.
Step 3
Move all terms containing to the left side of the equation.
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Step 3.1
Add to both sides of the equation.
Step 3.2
Combine the numerators over the common denominator.
Step 3.3
Simplify each term.
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Step 3.3.1
Apply the distributive property.
Step 3.3.2
Multiply by .
Step 3.3.3
Multiply by .
Step 3.4
Add and .
Step 3.5
Subtract from .
Step 3.6
Cancel the common factor of and .
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Step 3.6.1
Factor out of .
Step 3.6.2
Factor out of .
Step 3.6.3
Factor out of .
Step 3.6.4
Cancel the common factors.
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Step 3.6.4.1
Factor out of .
Step 3.6.4.2
Cancel the common factor.
Step 3.6.4.3
Rewrite the expression.
Step 3.7
Factor out of .
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Step 3.7.1
Factor out of .
Step 3.7.2
Factor out of .
Step 3.7.3
Factor out of .
Step 4
Set the numerator equal to zero.
Step 5
Solve the equation for .
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Step 5.1
Divide each term in by and simplify.
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Step 5.1.1
Divide each term in by .
Step 5.1.2
Simplify the left side.
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Step 5.1.2.1
Cancel the common factor of .
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Step 5.1.2.1.1
Cancel the common factor.
Step 5.1.2.1.2
Divide by .
Step 5.1.3
Simplify the right side.
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Step 5.1.3.1
Divide by .
Step 5.2
Add to both sides of the equation.