How do you solve this?

Question

11) 4/y-2 +1/y
12) 1/x^2-9 - 5/6+3a
13) 4/4-a^2 - 5/6+3a
14) 9/y-1/4=1/5
15) 12/x-12/x-2= -3

Answer 1

11 to 13 cannot be solved because the = is missing.

14) 9/y-1/4=1/5
[left and right x 20y]
180 - 5y = 4
176 -5y = 0
176 = 5y
y = 176/5

15) 12/x-12/x-2= -3
0 = -3+2.
This has no solution. This is wrong for any x.

Maybe the equation is
12/x-12/(x-2)= -3
Left and right times x(x-2)
12(x-2) - 12x = -3
12x - 24 - 12x = -3
-24 = -3
Also this has no solution. This is wrong for any x.

Answer 2

I'll solve number 15 with comment so you can do the other 4.

12/x - 12/(x-2) = -3 did I put the parenthesis right?

Multiply the two denominator and that will be the new denominator of the terms on the left side. Just like adding simple fractions, the new numerator = new deno. divided by old denominator times old numerator:

12(x-2) / x(x-2) - 12x / x(x-2) = -3

Combine:

(12x -24 -12x) / x(x-2) = -3

-24 / x(x-2) = -3

invert:

x(x-2) / -24 = -3

x(x-2) = -3 (-24)

x^2 - 2x + 72 = 0

Your in a tight place. This one has no rational solution for x. Use the quadratic formula to solve for x.

Answer 3

11) add 4/y to 1/y and subtract 2 (5/y-2)
13) 4/4=1 so 1-5/6-a^2+3a= -a^2+3a+1/6 (from there use solve like a quadratic)
14) 9/y-1/4-1/5=180y/20y-5y/20y-4y/20y= 171y/20y= 171/20
15) No real answer as far as i can see

Answer 4

Here's the thing do you really want an explanation of "how to solve" it, or do you just want the answer for your homework?