please check these answers

[sarahj3]

i am getting a little lost on these problems please check my answers

slove
1.) 2x/x+4=3/x-1
3(x+4)=(2x) (x-1)
3x+12=2x^2-2x
2x^2-5x-12=0
3x-12=0
3x=12
x=4

2.)4x/x-3-3=3x-1/x-3
x-3/1*4x-/x-3-x-3/1*3/1=x-3/1*3x-1/x-3
4x-3x-9=3x-1
1x-9=3x-1
3x-1x-8=0
2x-8=0
2x=8
x=4

3.)2+3/x=x
x(2+3/x)=x*x
5=x2 x2=5

4.)6/3y+3/y=1
3y*6/3y+3y*3/y=3y*1
6+9=3y
15=3y
y=5

5.)y/y+4+y/y+4=3
y+4*y/y+4+y+4*y+4=y+4*3
2y=y+4*3
2y=y=12
y=6

6.) write the rational expression x^2+x-42/36-12x+x^2 in lowest terms.
x^3/36-12x^3

add
7.) x+1/x^2-4x-5+x/x^2-5x-6+0 not sure what to do

8.) 3+2/x2
x^2*3+x^2*2/x^2
3x^2+2

multiply
9.)2x^6yz^7/-6x^8z*-20x^4y^3/x^3 not sure what to do

divide
10.) 4x-8/x-9/x^2-8x-9/x^2-4
flip second 4x-8/x-9*x^2-4/x^2-8x-9
4(x-2)/x-9*(x-2(x+2)/(x-9)(x+1)

11.) if y+19x^3+2/x^3-x, what values can x not have? not sure what to do

add
12.)7x/x+8+56/x+8
7x+56/x+8=7x+7

13.)x+15/27+12/27
x+27/27 =x=1

14.)7x-1/x^2+4x-12-3x+11/X2+4x-12
7x-1-3x+11/x^2+4x-12
4x-12/x^2+4x-12 =x2

15.)x/x-1-1/x+1
2x/x+4=3/x-1

thank you

 

[Denis]

i am getting a little lost on these problems please check my answers
1.) 2x/x+4=3/x-1
3(x+4)=(2x) (x-1)
3x+12=2x^2-2x

That's correct SO FAR; why are you stopping there?
2x^2 - 5x - 12 = 0 : now solve for x

 

[sarahj3]

i am getting a little lost on these problems please check my answers
1.) 2x/x+4=3/x-1
3(x+4)=(2x) (x-1)
3x+12=2x^2-2x

That's correct SO FAR; why are you stopping there?
2x^2 - 5x - 12 = 0 : now solve for x

thank you i see
3x-12=0
3x/3=12/3
x=4

 

[sarahj3]

i am getting a little lost on these problems please check my answers
1.) 2x/x+4=3/x-1
3(x+4)=(2x) (x-1)
3x+12=2x^2-2x

That's correct SO FAR; why are you stopping there?
2x^2 - 5x - 12 = 0 : now solve for x

thank you i see
3x-12=0
3x/3=12/3
x=4

i am hoping i did these first to right i am not sure. i just want to make sure i am on the right track ... thank you denis for helping me with the first one

 

[Mrspi]

i am getting a little lost on these problems please check my answers

slove
3.)2+3/x=x
x(2+3/x)=x*x
5=x2 x2=5



6.) write the rational expression x^2+x-42/36-12x+x^2 in lowest terms.
x^3/36-12x^3

thank you

First of all, when you post problems like this online, you need to CLEARLY show what is in the numerator and denominator of each fraction. While the problems stated in your text can show "what is OVER what" by using multiple lines, that doesn't work so well here. So please, in the future, please enclose the terms of each numerator and each denominator in parentheses.

For problem 3, do you mean this?
2 + (3/x) = x

If so, then your solution is not correct. The common denominator for all of the fractions is x. Multiply both sides by x:
x(2) + x(3/x) = x(x)
2x + 3 = x²

This is a quadratic equation, so let's get 0 on the left-hand side of the equation:

0 = x² - 2x - 3

Factor the right-hand side:

0 = (x - 3)(x + 1)

Set each factor equal to 0, and solve for x.
If x - 3 = 0, then x = 3.
If x + 1 = 0, then x = -1
So, the solutions are x = 3 or x = -1. You can check each solution by substituting into the original equation.

For problem 6, factor the numerator and factor the denominator:

(x + 7)(x - 6)
----------------
(6 - x)(6 + x)

Note that (x - 6) and (6 - x) are opposites. You can write (x - 6) as -1(6 - x). So, now we can write the problem this way:

-1(6 - x)(x + 7)
-------------------
(6 - x)(6 + x)

You have a common factor of (6 - x) in the numerator and denominator. Divide out this common factor to get

-1(x + 7)
------------
(6 + x)

Since the numerator and denominator have no other common factors, you are done.

I hope this helps you.