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How do you simplify #(4x^2+y)/(x+y) + (x^2-y^2)/(x+y)#?

Answer 1

Eva Abramson

#(4x^2+y)/(x+y)+x-y#

Simplify:

#(4x^2+y)/(x+y)+(x^2-y^2)/(x+y)#

Use difference of squares:

#(a^2-b^2)=(a+b)(a-b)#,

where: #a=x# and #b=y#.

#(4x^2+y)/(x+y)+(color(red)cancel(color(black)((x+y)))^1(x-y))/color(red)cancel(color(black)((x+y)))^1#

#(4x^2+y)/(x+y)+x-y#

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Answer 2

Genesis Allen

To simplify the expression (4x^2+y)/(x+y) + (x^2-y^2)/(x+y), we can combine the two fractions by finding a common denominator, which in this case is (x+y). Then, we add the numerators together and keep the common denominator. The simplified expression is (4x^2 + y + x^2 - y^2)/(x + y).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.