Simplifying Rational Expressions?

Question

1.) 7/x+3
x=
a. -3
b. -3 or 3
c. 3

2.)
16x^2 - 4x/3 - x
x=
a. 3
b. -3 or 3
c. 3

3.)
9x+2/x2 + 11x + 30
x=
a. -6 or -5
b. -4 or -7
c. 7 or 6

4: Simplify these rational expressions:
6y^2 + 18y/ 2y^3 - 6y^2 - 36y
a. 4y/y+4
b. 2/y
c. 3/y-6

5.
y^2 + 3y - 4/ 7y^3 + 7y^2 - 14y
a. y+4/7y(y+2)
b. y/ 8y(y + 2)
c. y+3/7(y^2 - 2)

Answer 1

Your first three questions don't make any sense. You can't find what x is equal to unless you have the expression equal to something.

4)
(6y^2 + 18y) / (2y^3 - 6y^2 - 36y)

Factor each part of the fraction:
6y^2 + 18y = 6y (y + 3)

2y^3 - 6y^2 - 36y
= 2y (y^2 - 3y - 18)
= 2y (y - 6)(y + 3)

Now you have:
[6y (y + 3)] / [2y (y - 6)(y + 3)]
= 3 / (y - 6)

5)
(y^2 + 3y - 4) / (7y^3 + 7y^2 - 14y)
= [(y + 4)(y - 1)] / [7y (y^2 + y - 2)]
= [(y + 4)(y - 1)] / [7y (y + 2)(y - 1)]
= (y + 4) / 7y(y + 2)

Answer 2

These aren't equations. You have to set them equal to something. Are these things equal to 0? Are they equal to 23?

Also, you need to specify what is in the denominator. For example, in problem 5, is that 3rd term (4/7) * y^3 or is it 4/(7y^3). You'll get very different answers.