Question

solve the rational equation. check your answer.
5/ 2x - 3 = 7/3x

Answer 1

15x=14x-21 do the equation

Answer 2

x=-21

Answer 3

\(\dfrac{5}{2x-3} = \dfrac{7}{3x}\)

Is that it?

#1 Domain Issues.

\(2x-3\ne 0\;and\;x\ne0 \)

Now what?

Answer 4

@tkhunny there's no domaine issue

Answer 5

#1 Domain Issues.
#2 Anyone who says there are no Domain Issues is being careless.

Now what?

Answer 6

The final answer should be -21, I just need to know how to show my work.

Answer 7

You show your work by showing your work.

You must not EVER multiply by ANYTHING unless you KNOW it is NOT zero. This is why there are Domain Issues.

\(\dfrac{5}{2x-3} = \dfrac{7}{3x}\)

In this form, it should be clear that a value x = 0 is unacceptable. Once we say that, we can multiply by x, giving.

\(\dfrac{5x}{2x-3} = \dfrac{7}{3}\)

3 is never zero, so we can multiply by that.

\(\dfrac{15x}{2x-3} = 7\)

In this form, it should be clear that 2x-3 = 0 is not acceptable. Once we say \(x\ne 3/2\), we can multiply by 2x-3, giving

\(15x = 7(2x-3)\)

Unfortunately, if I keep typing, you will only be able to show MY work. You do the rest.

Answer 8

I don't know how to continue

Answer 9

I think what @tkhunny was implying is that look at all parts of the problem, ifyou have a variable in the denominator find out what it means when they mentioned that \(\large x \neq \frac{ 3 }{ 2 }\) that means there will be a vertical asymptote at (3/2), hence the "domain issue" so now we're given \[15x=7(2x-3) \]\(15x=14x-21\) solve for x

Answer 10

Thank you

Answer 11

No problem