How do you simplify #(x^2 + 4x +4)/(x^2 + 7x +10) *( x^2 + 5x)/(x^2 + 6x + 8 )#?

Answer 1

You first factorise and see what you can cancel

#=((x+2)^2)/((x+2)(x+5))*(x(x+5))/((x+2)(x+4))#
We first note the restrictions #x!=-2andx!=-4andx!=-5# as this would make denominator(s) #=0#

Now we can cancel:

#=(cancel((x+2))(x+2))/(cancel((x+2))(x+5))*(x(x+5))/((x+2)(x+4))#
#=(xcancel((x+2))cancel((x+5)))/(cancel((x+2))(x+4)cancel((x+5)))#
#=x/(x+4)#
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Answer 2

To simplify the expression (x^2 + 4x + 4)/(x^2 + 7x + 10) * (x^2 + 5x)/(x^2 + 6x + 8), we can factorize the numerator and denominator of each fraction and then cancel out any common factors.

First, let's factorize the numerator and denominator of each fraction:

Numerator 1: x^2 + 4x + 4 = (x + 2)(x + 2) Denominator 1: x^2 + 7x + 10 = (x + 5)(x + 2)

Numerator 2: x^2 + 5x = x(x + 5) Denominator 2: x^2 + 6x + 8 = (x + 4)(x + 2)

Now, we can cancel out the common factors:

(x + 2) from the numerator of the first fraction and the denominator of the second fraction.

After canceling out the common factors, the expression simplifies to:

(x + 2)/(x + 5) * x/(x + 4)

Therefore, the simplified expression is (x + 2)/(x + 5) * x/(x + 4).

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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.

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.

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.

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.

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