Math help?

Question

4y / y^2-49 + y / y-7 Simplify if possible

Answer 1

Notice that y^2-49 = (y+7)(y-7)

Now multiply y/(y+7) by (y+7)/(y+7) to get a common denominator:

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

Rewrite as (4y + y^2 + 7y) / (y^2-49)

Finally rewrite as (y^2+11y) / (y^2-49)

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Answer 2

Multiply through by the lowest common denominator: y^2(y-7)...

4y(y-7) - 49y^2(y-7) +y^3

Multiply products - watch out for those double negatives!

4y^2 - 28y -49y^3 + 343y^2 +y^3

Combine like terms arranging by exponent

-48y^3 + 347y^2 - 28y

I left in simple polynomial form.