Simplify x/(x-1)+(2x-1)/(x^2-3x+2)

Factor using the AC method.
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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 .
Write the factored form using these integers.
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 .
Reorder the factors of .
Combine the numerators over the common denominator.
Simplify the numerator.
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Apply the distributive property.
Multiply by .
Move to the left of .
Add and .
Add and .
Rewrite in a factored form.
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Rewrite as .
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Simplify x/(x-1)+(2x-1)/(x^2-3x+2)

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Charlie Trom

Lucy Evel

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