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How do you simplify #(y+2) /(y^2+2y-48) div(y+2)/(y^2-13y+42 )#?

Answer 1

Abigail Allen

When dividing fractions we Keep Flip Change (KFC!)

Keep the first fraction the same

#[y+2]/[y^2+2y-48]#

Flip the second fraction

#[y^2-13y+42]/[y+2]#

Change the #-:# sign to #xx#

#[y+2]/[y^2+2y-48] xx [y^2-13y+42]/[y+2]#

factorise

#[y+2]/[(y+8)(y-6)] xx [(y-6)(y-7)]/[y+2]#

cancel #(y-6)#

#[y+2]/(y+8) xx (y-7)/[y+2]#

cancel #(y+2)#

#1/(y+8) xx (y-7)/1#

multiply

#(y-7)/(y+8)#

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Answer 2

Isaiah Anthony

To simplify the expression (y+2) /(y^2+2y-48) divided by (y+2)/(y^2-13y+42), we can multiply the first fraction by the reciprocal of the second fraction.

Reciprocal of (y+2)/(y^2-13y+42) is (y^2-13y+42)/(y+2).

So, the simplified expression is (y+2) /(y^2+2y-48) multiplied by (y^2-13y+42)/(y+2).

Now, we can cancel out the common factors in the numerator and denominator.

After canceling out the common factor (y+2), the simplified expression is (y^2-13y+42)/(y^2+2y-48).

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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.