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How do you find the quotient of #(r+2)/(r+1)div4/(r^2+3r+2)#?

Answer 1

Isaiah Anthony

#= (r + 2)^2/4#

#(r + 2)/(r + 1 ) -: 4 / (r^2 + 3 r + 2)#

change a sign #-:# to * (multiplication) and the location of #4 / (r^2 + 3 r + 2)#

# = (r + 2)/(r + 1 ) * (r^2 + 3 r + 2)/ 4#

factorize #(r^2 + 3 r + 2)#

#= (r + 2)/cancel(r + 1 ) * ((r+ 2)cancel((r + 1)))/ 4#

#= (r + 2)^2/4#

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Answer 2

Jace Anderson

To find the quotient of (r+2)/(r+1) divided by 4/(r^2+3r+2), we can simplify the expression by multiplying the numerator by the reciprocal of the denominator.

First, let's simplify the expression (r+2)/(r+1) by multiplying both the numerator and denominator by (r+1):

(r+2)/(r+1) * (r+1)/(r+1) = (r+2)(r+1)/(r+1)(r+1) = (r^2+3r+2)/(r^2+2r+1)

Now, we can divide this expression by 4/(r^2+3r+2) by multiplying the numerator by the reciprocal of the denominator:

(r^2+3r+2)/(r^2+2r+1) * (r^2+3r+2)/4 = (r^2+3r+2)^2/(4(r^2+2r+1))

Therefore, the quotient of (r+2)/(r+1) divided by 4/(r^2+3r+2) is (r^2+3r+2)^2/(4(r^2+2r+1)).

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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.