Perform the indicated operations and simplify y-4/y-7 - y+1/y+7 + y-49/y^2-49?

Question

I do not know how to do this problem at all. Can someone help me please

Answer 1

first get the LCD of the three terms.

the LCD is (y+7)(y-7)

then simplify

(y+7)(y-4) - (y+1)(y-7) + (y-49)

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             (y-7)(y+7)

by expanding you'll get:

y^2+3y-28-y^2+6y+7+y-49

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           (y-7)(y+7)

then by adding same terms you'll get:

10y-70

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(y-7)(y+7)

factor out 10:

10(y-7)

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(y-7)(y+7)

cancel out y-7

you'll get  10/y+7 and this is the answer i guess?hehe

Answer 2

first recognize that y^2 -49 = (y+7)(y-7)

common denominator is (y+7)(y-7)

y-4(y+7) - (y+1)(y-7) +  y-49/(y+7)(y-7)

y^2 +7y-4y-28 -( y^2 -6y-7) +  y-49/(y+7)(y-7)

y^2+3y-28-y^2+6y+7+y-49/y+7)(y-7)

10y-70/y+7)(y-7)

factor 10(y-7)/y+7)(y-7)

simplify 10/(y+7)

as long as y does not equal -7