#### danj

##### New member
The question says the given equation is either linear or equivalent to a linear equation. Solve the equation

sqrt 3x + sqrt 12 = x+5/sqrt of 3

I was thinking of trying to rationalize the denominator? Could you help me out?

#### Ishuda

##### Elite Member
The question says the given equation is either linear or equivalent to a linear equation. Solve the equation

sqrt 3x + sqrt 12 = x+5/sqrt of 3

I was thinking of trying to rationalize the denominator? Could you help me out?
You should use grouping symbols so that the meaning of your expressions are clear. I assume the equation is
$$\displaystyle \sqrt{3}\,\, x\, + \sqrt{12}\, =\, \frac{x\, +\, 5}{\sqrt{3}}$$
or possibly
$$\displaystyle \sqrt{3}\,\, x\, + \sqrt{12}\, =\, x\, +\, \frac{5}{\sqrt{3}}$$.

In either case what would happen if you multiplied through by $$\displaystyle \sqrt{3}$$?

#### danj

##### New member
You should use grouping symbols so that the meaning of your expressions are clear. I assume the equation is
$$\displaystyle \sqrt{3}\,\, x\, + \sqrt{12}\, =\, \frac{x\, +\, 5}{\sqrt{3}}$$
or possibly
$$\displaystyle \sqrt{3}\,\, x\, + \sqrt{12}\, =\, x\, +\, \frac{5}{\sqrt{3}}$$.

In either case what would happen if you multiplied through by $$\displaystyle \sqrt{3}$$?
I'm having a lot of trouble.
I got
=3x + 3 + (sq 3 x 2) = sqrt 3 (x+5) / sqrt 3

sorry I am having trouble using grouping symbols

#### stapel

##### Super Moderator
Staff member
I'm having a lot of trouble.
Please show your steps, so we can see where you're "having a lot of trouble", and try to figure out what is causing the difficulty.

I got
=3x + 3 + (sq 3 x 2) = sqrt 3 (x+5) / sqrt 3
What is on the left-hand side of the "equals" sign?

sorry I am having trouble using grouping symbols
They're just parentheses, brackets, or braces; they're just characters which group things together. And, until we know what the intended grouping is, we cannot be sure what you're saying. Sorry.

The question says the given equation is either linear or equivalent to a linear equation. Solve the equation

sqrt 3x + sqrt 12 = x+5/sqrt of 3
Working on the left-hand side of the equation, do you mean either of the following?

. . . . .$$\displaystyle \mbox{a. }\, \sqrt{\strut 3x\,}\, +\, \sqrt{\strut 12\,}$$

. . . . .$$\displaystyle \mbox{b. }\, \sqrt{\strut 3\,}\, x\, +\, \sqrt{\strut 12\,}$$

Working on the right-hand side of the equation, so you mean either of the following?

. . . . .$$\displaystyle \mbox{c. }\, x\, +\, \dfrac{5}{\sqrt{\strut 3\,}}$$

. . . . .$$\displaystyle \mbox{d. }\, \dfrac{x\, +\, 5}{\sqrt{\strut 3\,}}$$

It was suggested that you try multiplying through by the square root of three. In your reply, the first part of your "equation" (the part that followed the first "equals" sign) seems to have four terms. Since the original equation appeared only to have two terms on the left-hand side, clearly there is some confusion somewhere.

When you reply, please show all of your steps. Thank you! 