Finite Math Examples

Solve for x 40x-39=40/x
Step 1
Add to both sides of the equation.
Step 2
Find the LCD of the terms in the equation.
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Step 2.1
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Step 2.2
The LCM of one and any expression is the expression.
Step 3
Multiply each term in by to eliminate the fractions.
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Step 3.1
Multiply each term in by .
Step 3.2
Simplify the left side.
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Step 3.2.1
Multiply by by adding the exponents.
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Step 3.2.1.1
Move .
Step 3.2.1.2
Multiply by .
Step 3.3
Simplify the right side.
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Step 3.3.1
Cancel the common factor of .
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Step 3.3.1.1
Cancel the common factor.
Step 3.3.1.2
Rewrite the expression.
Step 4
Solve the equation.
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Step 4.1
Subtract from both sides of the equation.
Step 4.2
Subtract from both sides of the equation.
Step 4.3
Factor by grouping.
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Step 4.3.1
For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
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Step 4.3.1.1
Factor out of .
Step 4.3.1.2
Rewrite as plus
Step 4.3.1.3
Apply the distributive property.
Step 4.3.2
Factor out the greatest common factor from each group.
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Step 4.3.2.1
Group the first two terms and the last two terms.
Step 4.3.2.2
Factor out the greatest common factor (GCF) from each group.
Step 4.3.3
Factor the polynomial by factoring out the greatest common factor, .
Step 4.4
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 4.5
Set equal to and solve for .
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Step 4.5.1
Set equal to .
Step 4.5.2
Solve for .
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Step 4.5.2.1
Subtract from both sides of the equation.
Step 4.5.2.2
Divide each term in by and simplify.
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Step 4.5.2.2.1
Divide each term in by .
Step 4.5.2.2.2
Simplify the left side.
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Step 4.5.2.2.2.1
Cancel the common factor of .
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Step 4.5.2.2.2.1.1
Cancel the common factor.
Step 4.5.2.2.2.1.2
Divide by .
Step 4.5.2.2.3
Simplify the right side.
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Step 4.5.2.2.3.1
Move the negative in front of the fraction.
Step 4.6
Set equal to and solve for .
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Step 4.6.1
Set equal to .
Step 4.6.2
Solve for .
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Step 4.6.2.1
Add to both sides of the equation.
Step 4.6.2.2
Divide each term in by and simplify.
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Step 4.6.2.2.1
Divide each term in by .
Step 4.6.2.2.2
Simplify the left side.
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Step 4.6.2.2.2.1
Cancel the common factor of .
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Step 4.6.2.2.2.1.1
Cancel the common factor.
Step 4.6.2.2.2.1.2
Divide by .
Step 4.7
The final solution is all the values that make true.
Step 5
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Mixed Number Form: