solve: 3x/2+1/x=3x/4

Question

shadowfiend · Answer

The first move would be to multiply through by x:

3x^2 / 2 + 1 = 3x^2 / 4

Then multiply through by 4:

6x^2 + 4 = 3x^2

Can you solve that?

anonymous · Answer

what do you mean multiply through by x?

shadowfiend · Answer

We multiply both sides by x, so that we can get x out of the denominator in 1 / x.

anonymous · Answer

arent you looking for a common denominator of 2x though?

shadowfiend · Answer

Hm? No, you can just multiply both sides by x, and that'll cancel the x out in the denominator on the left, and make the other two x-es x^2s instead.

anonymous · Answer

i dont understand what your saying

shadowfiend · Answer

The easiest way to solve an equation like this is to make sure there is no x in any denominators.

anonymous · Answer

ok so multiply everything by x/x?

anonymous · Answer

i dont really understand i thought you would multiply everything by 2x to get a common denominator and then add the left side?

anonymous · Answer

there are multiple ways to approach this problem.  finding common denominator for LHS of equation and cross multiplying is also another way.

anonymous · Answer

ok can you show me steps on how to solve this equation please

shadowfiend · Answer

You don't have to multiply by x/x, you can just multiply by x. For example:

5 = 5
x*5 = x*5
5x = 5x

So the equation is still valid. In this case:

$$\frac{3x}{2}+\frac{1}{x} = \frac{3x}{4}$$
$$x\left(\frac{3x}{2}+\frac{1}{x}\right) = x\frac{3x}{4}$$
$$\frac{x\cdot 3x}{2} + \frac{x\cdot 1}{x} = \frac{x\cdot 3x}{4}$$
$$\frac{3x^2}{2} + \frac{x}{x} = \frac{3x^2}{4}$$
$$\frac{3x^2}{2} + 1 = \frac{3x^2}{4}$$

(And Min-hee is correct about there being multiple approaches; just trying to explain mine. Have to go now though, sorry.)

anonymous · Answer

you can multiply both sides of equations by x, 2x or 4x.  All of which should give you the same answer

anonymous · Answer

thank you i got the answer..can you take a look at my other problems?