# Expressing rational expressions in its lowest terms

#### poisonposey

##### New member
Hello. I seem to be having issues reducing these problems.
x/x+xy which I end up getting 1/xy for the lowest.
3x^2=6x/3x^2+9 which I keep getting it broken down to: 3x(x+2)/3x(x+3)= x-3*x-2
x=-3,-2
I'm not sure if I am doing this correctly or not.

#### masters

##### Full Member
poisonposey said:
Hello. I seem to be having issues reducing these problems.
x/x+xy which I end up getting 1/xy for the lowest.
3x^2=6x/3x^2+9 which I keep getting it broken down to: 3x(x+2)/3x(x+3)= x-3*x-2
x=-3,-2
I'm not sure if I am doing this correctly or not.
For the first one, I think you mean:

$$\displaystyle \frac{x}{x+xy}=\frac{x}{x(1+y)}=\frac{1}{1+y}$$

For the second one you're going to have to use grouping symbols for us to better understand what you mean.

As written, it could be:

$$\displaystyle 3x^2=\frac{6x}{3x^2+9}$$

or

$$\displaystyle 3x^2=\frac{6x}{3x^2}+9$$

#### mmm4444bot

##### Super Moderator
Staff member
poisonposey said:
3x^2=6x/3x^2+9 which I keep getting it broken down to: 3x(x+2)/3x(x+3)= x-3*x-2

x = -3, -2

From your work shown, I think you made a typographical error when typing the original expression.

(3x^2 + 6x)/(3x^2 + 9)

Your first step is good, but you did not properly factor the denominator. (Or, perhaps you made another typographical error on the original expression by typing 9 instead of 9x).

[3x(x + 2)]/[3(x + 3)]

Now, the factor of 3 above cancels with the factor of 3 below.

[x(x + 2)]/(x + 3)

Since this is not an equation, there is no way to solve for x.

You tried to solve for x, at the end of your work. I'm not sure why because you stated the instruction as express rational expressions in lowest terms.

#### poisonposey

##### New member
Re:

mmm4444bot said:
poisonposey said:
3x^2=6x/3x^2+9 which I keep getting it broken down to: 3x(x+2)/3x(x+3)= x-3*x-2

x = -3, -2

From your work shown, I think you made a typographical error when typing the original expression.

(3x^2 + 6x)/(3x^2 + 9)

Your first step is good, but you did not properly factor the denominator. (Or, perhaps you made another typographical error on the original expression by typing 9 instead of 9x).

[3x(x + 2)]/[3(x + 3)]

Now, the factor of 3 above cancels with the factor of 3 below.

[x(x + 2)]/(x + 3)

Since this is not an equation, there is no way to solve for x.

You tried to solve for x, at the end of your work. I'm not sure why because you stated the instruction as express rational expressions in lowest terms.

I did type it incorrectly. It is 3x^2+6x/ 3x^2+9x I thought that I had to solve for x. I am so lost in this subject. I am doing this all online, so I don't get much feed back on whether or not I am doing this correctly. I have about 11 more equations and I think I can only solve 4 correctly. :?

#### Denis

##### Senior Member
Re: Re:

poisonposey said:
I did type it incorrectly. It is 3x^2+6x/ 3x^2+9x
That is still not correctly shown; should be: (3x^2 + 6x) / (3x^2 + 9x) ; brackets VERY important.

With no brackets, what you show is equivalent to 3x^2 + 9x + 6x/(3x^2)

#### mmm4444bot

##### Super Moderator
Staff member
poisonposey said:
… I thought that I had to solve for x. I am so lost in this subject …

You need an equation before you can solve.

The instruction to express in lowest terms means simplify; there is nothing to solve.