Pre-Algebra Examples

Solve for a (3a)/(a+16)=a/(a-19)
Step 1
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 2
Solve the equation for .
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Step 2.1
Simplify .
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Step 2.1.1
Rewrite.
Step 2.1.2
Simplify by adding zeros.
Step 2.1.3
Apply the distributive property.
Step 2.1.4
Multiply by by adding the exponents.
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Step 2.1.4.1
Move .
Step 2.1.4.2
Multiply by .
Step 2.1.5
Multiply by .
Step 2.2
Simplify .
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Step 2.2.1
Apply the distributive property.
Step 2.2.2
Multiply by .
Step 2.3
Move all terms containing to the left side of the equation.
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Step 2.3.1
Subtract from both sides of the equation.
Step 2.3.2
Subtract from both sides of the equation.
Step 2.3.3
Subtract from .
Step 2.3.4
Subtract from .
Step 2.4
Factor out of .
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Step 2.4.1
Factor out of .
Step 2.4.2
Factor out of .
Step 2.4.3
Factor out of .
Step 2.5
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 2.6
Set equal to .
Step 2.7
Set equal to and solve for .
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Step 2.7.1
Set equal to .
Step 2.7.2
Solve for .
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Step 2.7.2.1
Add to both sides of the equation.
Step 2.7.2.2
Divide each term in by and simplify.
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Step 2.7.2.2.1
Divide each term in by .
Step 2.7.2.2.2
Simplify the left side.
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Step 2.7.2.2.2.1
Cancel the common factor of .
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Step 2.7.2.2.2.1.1
Cancel the common factor.
Step 2.7.2.2.2.1.2
Divide by .
Step 2.8
The final solution is all the values that make true.
Step 3
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Mixed Number Form: