Simplify (y^2-7y+6)/(-4y^2+8y-4)

Math
y2-7y+6-4y2+8y-4
Factor y2-7y+6 using the AC method.
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Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is 6 and whose sum is -7.
-6,-1
Write the factored form using these integers.
(y-6)(y-1)-4y2+8y-4
(y-6)(y-1)-4y2+8y-4
Simplify the denominator.
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Factor 4 out of -4y2+8y-4.
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Factor 4 out of -4y2.
(y-6)(y-1)4(-y2)+8y-4
Factor 4 out of 8y.
(y-6)(y-1)4(-y2)+4(2y)-4
Factor 4 out of -4.
(y-6)(y-1)4(-y2)+4(2y)+4(-1)
Factor 4 out of 4(-y2)+4(2y).
(y-6)(y-1)4(-y2+2y)+4(-1)
Factor 4 out of 4(-y2+2y)+4(-1).
(y-6)(y-1)4(-y2+2y-1)
(y-6)(y-1)4(-y2+2y-1)
Factor by grouping.
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For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=-1⋅-1=1 and whose sum is b=2.
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Factor 2 out of 2y.
(y-6)(y-1)4(-y2+2(y)-1)
Rewrite 2 as 1 plus 1
(y-6)(y-1)4(-y2+(1+1)y-1)
Apply the distributive property.
(y-6)(y-1)4(-y2+1y+1y-1)
Multiply y by 1.
(y-6)(y-1)4(-y2+y+1y-1)
Multiply y by 1.
(y-6)(y-1)4(-y2+y+y-1)
(y-6)(y-1)4(-y2+y+y-1)
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
(y-6)(y-1)4((-y2+y)+y-1)
Factor out the greatest common factor (GCF) from each group.
(y-6)(y-1)4(y(-y+1)-1(-y+1))
(y-6)(y-1)4(y(-y+1)-1(-y+1))
Factor the polynomial by factoring out the greatest common factor, -y+1.
(y-6)(y-1)4((-y+1)(y-1))
(y-6)(y-1)4(-y+1)(y-1)
Combine exponents.
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Factor -1 out of -y.
(y-6)(y-1)4(-(y)+1)(y-1)
Rewrite 1 as -1(-1).
(y-6)(y-1)4(-(y)-1(-1))(y-1)
Factor -1 out of -(y)-1(-1).
(y-6)(y-1)4(-(y-1))(y-1)
Rewrite -(y-1) as -1(y-1).
(y-6)(y-1)4(-1(y-1))(y-1)
Raise y-1 to the power of 1.
(y-6)(y-1)4⋅-1((y-1)1(y-1))
Raise y-1 to the power of 1.
(y-6)(y-1)4⋅-1((y-1)1(y-1)1)
Use the power rule aman=am+n to combine exponents.
(y-6)(y-1)4⋅-1(y-1)1+1
Add 1 and 1.
(y-6)(y-1)4⋅-1(y-1)2
Multiply 4 by -1.
(y-6)(y-1)-4(y-1)2
(y-6)(y-1)-4(y-1)2
(y-6)(y-1)-4(y-1)2
Reduce the expression by cancelling the common factors.
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Cancel the common factor of y-1 and (y-1)2.
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Factor y-1 out of (y-6)(y-1).
(y-1)(y-6)-4(y-1)2
Cancel the common factors.
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Factor y-1 out of -4(y-1)2.
(y-1)(y-6)(y-1)(-4(y-1))
Cancel the common factor.
(y-1)(y-6)(y-1)(-4(y-1))
Rewrite the expression.
y-6-4(y-1)
y-6-4(y-1)
y-6-4(y-1)
Move the negative in front of the fraction.
-y-64(y-1)
-y-64(y-1)
Simplify (y^2-7y+6)/(-4y^2+8y-4)

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