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If l is not equal to −3 or −4, then l/l + 4 + 3/l + 3 =

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If l is not equal to −3 or −4, then l/l + 4 + 3/l + 3 =  [#permalink]

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New post 27 Feb 2019, 23:52
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If l is not equal to −3 or −4, then \(\frac{l}{l + 4} + \frac{3}{l + 3} =\)


A. 1

B. \(\frac{7}{l + 4}\)

C. \(\frac{l+3}{2l + 7}\)

D. \(\frac{3l}{(l + 4)(l + 2)}\)

E. \(\frac{l^2 + 6l + 12}{(l + 4)(l + 3)}\)

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Re: If l is not equal to −3 or −4, then l/l + 4 + 3/l + 3 =  [#permalink]

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New post 28 Feb 2019, 06:04
Bunuel wrote:
If l is not equal to −3 or −4, then \(\frac{l}{l + 4} + \frac{3}{l + 3} =\)


A. 1

B. \(\frac{7}{l + 4}\)

C. \(\frac{l+3}{2l + 7}\)

D. \(\frac{3l}{(l + 4)(l + 2)}\)

E. \(\frac{l^2 + 6l + 12}{(l + 4)(l + 3)}\)



solve for the given fractions
we get
\(\frac{l^2 + 6l + 12}{(l + 4)(l + 3)}\)
IMO E
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Re: If l is not equal to −3 or −4, then l/l + 4 + 3/l + 3 =  [#permalink]

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New post 28 Feb 2019, 15:01
1
Bunuel wrote:
If l is not equal to −3 or −4, then \(\frac{l}{l + 4} + \frac{3}{l + 3} =\)


A. 1

B. \(\frac{7}{l + 4}\)

C. \(\frac{l+3}{2l + 7}\)

D. \(\frac{3l}{(l + 4)(l + 2)}\)

E. \(\frac{l^2 + 6l + 12}{(l + 4)(l + 3)}\)


This one becomes relatively simple if you plug in 1 for the variable l.

If you plug in 1, the answer to the addition question is \(\frac{19}{20}\)

You can quickly eliminate answer A and B, since they clearly do not equal \(\frac{19}{20}\)
Answer E is the most logical choice to try next, because you know that you must have 19 in the numerator (at glance you can see that the numerators C and D
will not amount to 19).

BAM!
\(\frac{1^2 + 6(1) + 12}{(1+ 4)(1 + 3)}\)=\(\frac{1+6+12}{(5)(4)}\) =\(\frac{19}{20}\)

Answer: E
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Re: If l is not equal to −3 or −4, then l/l + 4 + 3/l + 3 =  [#permalink]

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New post 28 Feb 2019, 18:07
ckadams wrote:
Bunuel wrote:
If l is not equal to −3 or −4, then \(\frac{l}{l + 4} + \frac{3}{l + 3} =\)


A. 1

B. \(\frac{7}{l + 4}\)

C. \(\frac{l+3}{2l + 7}\)

D. \(\frac{3l}{(l + 4)(l + 2)}\)

E. \(\frac{l^2 + 6l + 12}{(l + 4)(l + 3)}\)


This one becomes relatively simple if you plug in 1 for the variable l.


Nice! It's also possible to plug in 0 for the variable \(l\).

In that case, the original value is 0/4 + 3/3 = 1.

Go through the answer choices, plugging in 0:

(A) 1 - could be correct
(B) 7/4 - wrong
(C) 3/7 - wrong
(D) 0 / something - wrong, because it'll come out to be 0
(E) 12/12 = 1 - could be correct

Of the two options (A) and (E), I'm going to choose (E) for sure, because I don't think the value of the expression will always come out to be the same no matter what I choose for l!
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Re: If l is not equal to −3 or −4, then l/l + 4 + 3/l + 3 =  [#permalink]

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New post 04 Mar 2019, 20:07
Bunuel wrote:
If l is not equal to −3 or −4, then \(\frac{l}{l + 4} + \frac{3}{l + 3} =\)


A. 1

B. \(\frac{7}{l + 4}\)

C. \(\frac{l+3}{2l + 7}\)

D. \(\frac{3l}{(l + 4)(l + 2)}\)

E. \(\frac{l^2 + 6l + 12}{(l + 4)(l + 3)}\)


Getting a common denominator of (l + 3)(l + 4), we have:

(l + 3)/(l + 3) x l/(l + 4) + (l + 4)/(l + 4) x 3/(l + 3)

(l^2 + 3l)/[(l + 3)(l + 4)] + (3l + 12)/[(l + 3)(l + 4)]

(l^2 + 6l + 12)/[(l + 3)(l + 4)]

Alternate Solution:

We notice that the given expression l/(l + 4) + 3/(l + 3) becomes 1 at l = 0. Therefore, we can eliminate answer choices B, C and D. To decide between answer choices A and E, let’s look at the value of l/(l + 4) + 3/(l + 3) at l = 1. Notice that we don’t need to evaluate the expression, we only need to notice that at l = 1, the given expression becomes 1/5 + 3/4, which is clearly not equal to 1. Therefore, we can eliminate answer choice A as well. The only remaining choice is E.

Answer: E
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Re: If l is not equal to −3 or −4, then l/l + 4 + 3/l + 3 =   [#permalink] 04 Mar 2019, 20:07
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