Pre-Algebra Examples

Solve by Graphing 11/(x+4)-(x-6)/(x-10)=(-x^2)/(x^2-6x-40)
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
Reorder the factors of .
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
Multiply by .
Step 1.5.3
Apply the distributive property.
Step 1.5.4
Multiply by .
Step 1.5.5
Expand using the FOIL Method.
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Step 1.5.5.1
Apply the distributive property.
Step 1.5.5.2
Apply the distributive property.
Step 1.5.5.3
Apply the distributive property.
Step 1.5.6
Simplify and combine like terms.
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Step 1.5.6.1
Simplify each term.
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Step 1.5.6.1.1
Multiply by by adding the exponents.
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Step 1.5.6.1.1.1
Move .
Step 1.5.6.1.1.2
Multiply by .
Step 1.5.6.1.2
Multiply by .
Step 1.5.6.1.3
Multiply by .
Step 1.5.6.2
Add and .
Step 1.5.7
Add and .
Step 1.5.8
Add and .
Step 1.5.9
Reorder terms.
Step 1.6
Simplify with factoring out.
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Step 1.6.1
Factor out of .
Step 1.6.2
Factor out of .
Step 1.6.3
Factor out of .
Step 1.6.4
Rewrite as .
Step 1.6.5
Factor out of .
Step 1.6.6
Simplify the expression.
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Step 1.6.6.1
Rewrite as .
Step 1.6.6.2
Move the negative in front of the fraction.
Step 2
Simplify .
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Step 2.1
Factor using the AC method.
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Step 2.1.1
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 2.1.2
Write the factored form using these integers.
Step 2.2
Move the negative in front of the fraction.
Step 3
Graph each side of the equation. The solution is the x-value of the point of intersection.
Step 4