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If x ≠ 1, which expression is equal to x(x − 1) − 2(x + 1) + 3(x + 5)/

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Bunuel
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If x ≠ 1, which expression is equal to x(x − 1) − 2(x + 1) + 3(x + 5)/ [#permalink] New post   20 Apr 2017, 23:41
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If x ≠ 1, which expression is equal to \(\frac{x(x − 1) − 2(x + 1) + 3(x + 5)}{(x − 1)}\) ?

A. (x^2 + 13)/(x − 1)

B. (x^2 + 17/(x − 1)

C. (x^2 + x + 12)/(x − 1)

D. (x^2 + x + 5)/(x − 1)

E. 13/(x − 1)
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quantumliner
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Re: If x ≠ 1, which expression is equal to x(x − 1) − 2(x + 1) + 3(x + 5)/ [#permalink] New post   21 Apr 2017, 01:25
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[x(x−1)−2(x+1)+3(x+5)]/(x-1)

above can be written as

[x^2 - x - 2x - 2 + 3x +15]/(x-1)

can be further simplified to

(x^2 + 13)/(x-1)

Answer is A. (x^2 + 13)/(x − 1)
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Re: If x ≠ 1, which expression is equal to x(x − 1) − 2(x + 1) + 3(x + 5)/ [#permalink] New post   21 Apr 2017, 02:58
x^2-x-2x-2+3x+15= (x^2+13)/(x-1)

When there is no pattern i.e. we can't relate the expression to any identity then simplify the expression as there are chances that some values would be cancelled.
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Re: If x ≠ 1, which expression is equal to x(x − 1) − 2(x + 1) + 3(x + 5)/ [#permalink] New post   23 Apr 2017, 12:56
Bunuel wrote:
If x ≠ 1, which expression is equal to \(\frac{x(x − 1) − 2(x + 1) + 3(x + 5)}{(x − 1)}\) ?

A. (x^2 + 13)/(x − 1)

B. (x^2 + 17/(x − 1)

C. (x^2 + x + 12)/(x − 1)

D. (x^2 + x + 5)/(x − 1)

E. 13/(x − 1)


Okay so in order to solve this question we can simply plug in a value for the given equation such as 3 and find an equation within the answers that yields the sam result.

If we examine (3)^2 + 13 / 2 = 11

Now if 3 into the top

3(3-1) - 2(3+1) + 3(3+5) / (3-1) =
3(2) - 2(4) + 3(8) / (2) =
6 - 8 + 24 / 2 = ( in is important to note PEMDAS does not actually apply in this scenario; because addition and subtraction are equal rank they are performed as they appear from left to right)
-2 + 24 /2 = 11

Thus A
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Re: If x ≠ 1, which expression is equal to x(x − 1) − 2(x + 1) + 3(x + 5)/ [#permalink] New post   25 Apr 2017, 07:52
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Bunuel wrote:
If x ≠ 1, which expression is equal to \(\frac{x(x − 1) − 2(x + 1) + 3(x + 5)}{(x − 1)}\) ?

A. (x^2 + 13)/(x − 1)

B. (x^2 + 17/(x − 1)

C. (x^2 + x + 12)/(x − 1)

D. (x^2 + x + 5)/(x − 1)

E. 13/(x − 1)


We can simplify the numerator of the given fraction and we have:

x^2 - x - 2x - 2 + 3x + 15 = x^2 + 13

Thus, we are left with (x^2 + 13)/(x - 1).

Answer: A
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Re: If x ≠ 1, which expression is equal to x(x − 1) − 2(x + 1) + 3(x + 5)/ [#permalink] New post   27 Apr 2017, 11:41
\(\frac{{x^2 - x - 2x - 2 + 3x + 15 }}{(x - 1)}\) ---> Simplify and we get below eq

\(\frac{{(x^2 + 13)}}{{(x - 1)}}\)

Ans: Option A
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Re: If x ≠ 1, which expression is equal to x(x − 1) − 2(x + 1) + 3(x + 5)/ [#permalink] New post   16 May 2017, 11:31
put x=0, and we will be left with option A and E.

E can't be the correct answer as the original expression has a power of 2.

hence correct answer is A
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Re: If x ≠ 1, which expression is equal to x(x − 1) − 2(x + 1) + 3(x + 5)/ [#permalink] New post   07 Jun 2018, 04:58
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Re: If x ≠ 1, which expression is equal to x(x − 1) − 2(x + 1) + 3(x + 5)/ [#permalink]
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