SAT practice test two section three number 15

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1

Hey everyone!

I can’t figure out this question. From the videos I found on YouTube and the SAT book, I’ve gathered that I’m supposed to divide the numerator by the denominator, but I don’t know how and it hasn’t been clearly explained. For those of you without the book, the question is:

The expression (5x-2)/(x+3) is equivalent to which of the following?
The answer is 5 - ((17)/(x+3))

Any help and explanations are much appreciated!

2

Expression can be written as (5x+15)/(x+3) - 17/(x+3) which is equal to 5 - 17/(x+3).

3

@greenteen17 Do you remember how to do long division? take 5x-2 divided by x+3

4

This is also an easy opportunity to go around to the back door: make up an x value – say x = 2.

Put that into the given expression and you get a value of 8/5 or 1.6. Then put x = 2 into each answer…you will only get one that matches.

5

@annamom I don’t remember ever doing long division with variables…feels really dumb

6

@greenteen17 I don’t know how to post it. But take 5x-2 divided by x+3, you will first have to put 5 as the quotient to get 5x +15 and you subtract 5x+15 from 5x-2… here is a video from Khanacademy
https://www.khanacademy.org/math/algebra-home/alg-polynomials/alg-long-division-of-polynomials/v/dividing-polynomials-1

this is what should be covered from Algebra 2…look at those books… I always told my kids to go back to the basics…

7

I meant basic from what they learned…

8

@greenteen17 it is fairly similar to doing long division with integers (such as 121 divided by 7), but a little more generalized.

There’s also another method called synthetic division which works for this problem (if you know the technique) – I never actually learned synthetic division in my algebra class, and have never needed to use it.

Of course, plugging in numbers is often a good strategy for SAT-like exams and might save you time if your algebra is a bit rusty.

9

Though I prefer the plug-in strategy for this problem, I would say long division would be my third choice, synthetic division fourth. I really like what @MITer94 mentioned earlier – it’s worth a closer look:

I hope my spacing doesn’t get screwed up…

You have:

(5x-2)

(x+3)

Is there something you could do to the numerator so that x+3 would divide it evenly? wouldn’t be nice if that -2 was a +15 instead? Re-write it as:

(5x+15)-17

(x+3)

Then it breaks into two terms very nicely, giving you the answer:

5 - (17)/(x+3)

This is almost like doing long division in your head. Very slick.

…but making up numbers is still easier!