Simplify (5q+1)/(4q^2+7q-2)-(2q+3)/(3q^2+5q-2)

Math
Simplify each term.
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Factor by grouping.
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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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Factor out of .
Rewrite as plus
Apply the distributive property.
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
Factor out the greatest common factor (GCF) from each group.
Factor the polynomial by factoring out the greatest common factor, .
Factor by grouping.
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For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
Tap for more steps…
Factor out of .
Rewrite as plus
Apply the distributive property.
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
Factor out the greatest common factor (GCF) from each group.
Factor the polynomial by factoring out the greatest common factor, .
To write as a fraction with a common denominator, multiply by .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Multiply and .
Multiply and .
Reorder the factors of .
Reorder the factors of .
Combine the numerators over the common denominator.
Simplify the numerator.
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Expand using the FOIL Method.
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Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
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Simplify each term.
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Multiply by .
Multiply by .
Multiply by .
Multiply by .
Multiply by .
Add and .
Apply the distributive property.
Multiply by .
Multiply by .
Expand using the FOIL Method.
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Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
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Simplify each term.
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Multiply by .
Multiply by .
Multiply by .
Multiply by .
Multiply by .
Subtract from .
Subtract from .
Subtract from .
Add and .
Simplify (5q+1)/(4q^2+7q-2)-(2q+3)/(3q^2+5q-2)
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