# Math Help - Adding Rational Expressions

1. ## Adding Rational Expressions

2(4x+1)/5x-7 + 3(x-2)7-5x + -10x -1/5x-7

The answer in the book is -1. The closest I've come to getting that number is

5x -3/5x-7

But obviously that's not write and I had to do some pretty creative things to come up with that number. I'm pretty sure my error is happening when multiplying the middle term by -1 but still, I'm not getting the right answer. Any help is appreciated. Thanks.

P.S. If there's a way to more easily write out mathematical terms on the computer, I'd like to know about it.

2. $\dfrac{2(4x+1)}{5x-7} + \dfrac{3(x-2)}{7-5x} + \dfrac{-10x -1}{5x-7}$

You'll need to switch the terms in the denominator of the 2nd fraction and then change the plus in front of the 2nd fraction to a minus:
$=\dfrac{2(4x+1)}{5x-7} - \dfrac{3(x-2)}{5x - 7} + \dfrac{-10x -1}{5x-7}$

$=\dfrac{2(4x+1) - 3(x-2) + (-10x -1)}{5x-7}$

$=\dfrac{8x + 2 - 3x + 6 - 10x - 1}{5x-7}$

$=\dfrac{-5x + 7}{5x-7}$

$=-\dfrac{5x-7}{5x-7}$

$=-1$

3. Originally Posted by Ingersoll
2(4x+1)/5x-7 + 3(x-2)7-5x + -10x -1/5x-7

The answer in the book is -1. The closest I've come to getting that number is

5x -3/5x-7

But obviously that's not write and I had to do some pretty creative things to come up with that number. I'm pretty sure my error is happening when multiplying the middle term by -1 but still, I'm not getting the right answer. Any help is appreciated. Thanks.

P.S. If there's a way to more easily write out mathematical terms on the computer, I'd like to know about it.

Hi Ingersoll,

This is what you have written:

$\frac{2(4x+1)}{5x}-7+3(x-2)7-5x+-10x-\frac{1}{5x}-7$

Apparently eumyang deciphered it, but it is majorly confusing. Use grouping symbols.

4. I look forward to more of your insightful help in the future. My apologies for leaving you so baffled by inadvertantly leaving out one grouping symbol in a problem with a stated answer and solution.

5. Originally Posted by Ingersoll
I look forward to more of your insightful help in the future. My apologies for leaving you so baffled by inadvertantly leaving out one grouping symbol in a problem with a stated answer and solution.

2(4x+1)/(5x-7) + 3(x-2)/(7-5x) + (-10x -1)/(5x-7)
... you left out four grouping symbols and a division sign.