Basic Math Examples

Solve for z z/(5z+18)=-3/z
Step 1
Move the negative in front of the fraction.
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 adding zeros.
Step 3.1.3
Multiply by .
Step 3.2
Simplify .
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Step 3.2.1
Apply the distributive property.
Step 3.2.2
Multiply.
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Step 3.2.2.1
Multiply by .
Step 3.2.2.2
Multiply by .
Step 3.3
Add to both sides of the equation.
Step 3.4
Add to both sides of the equation.
Step 3.5
Factor using the AC method.
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Step 3.5.1
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 3.5.2
Write the factored form using these integers.
Step 3.6
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 3.7
Set equal to and solve for .
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Step 3.7.1
Set equal to .
Step 3.7.2
Subtract from both sides of the equation.
Step 3.8
Set equal to and solve for .
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Step 3.8.1
Set equal to .
Step 3.8.2
Subtract from both sides of the equation.
Step 3.9
The final solution is all the values that make true.