Algebra Examples

Solve by Factoring 1+1/x=12/(x^2)
Step 1
Subtract from both sides of the equation.
Step 2
Reorder terms.
Step 3
To write as a fraction with a common denominator, multiply by .
Step 4
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 4.1
Multiply by .
Step 4.2
Multiply by .
Step 5
Combine the numerators over the common denominator.
Step 6
Write as a fraction with a common denominator.
Step 7
Combine the numerators over the common denominator.
Step 8
Factor using the AC method.
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Step 8.1
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Step 8.2
Write the factored form using these integers.
Step 9
Set the numerator equal to zero.
Step 10
Solve the equation for .
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Step 10.1
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 10.2
Set equal to and solve for .
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Step 10.2.1
Set equal to .
Step 10.2.2
Add to both sides of the equation.
Step 10.3
Set equal to and solve for .
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Step 10.3.1
Set equal to .
Step 10.3.2
Subtract from both sides of the equation.
Step 10.4
The final solution is all the values that make true.