Solve rational equations. Please help!

[School_girl]

3/(5x) + 7/(2x) = 1

Okey, this is a problem that I am having difficulties with. I have to find what x is equal to.

On my first try, I took all of the answers( that was given to me) and I put them on the place of x. For some reason, x = 10/41.......I put it in for x( 10/41) and it equaled to 1, however as I was told, it was wrong! Can anyone help me....

Thanks,

Me

 

[tkhunny]

3/(5x) + 7/(2x) = 1

Plugging-in is a very popular method. If all that is wanted are the solutions, plugging-in should be fine. If you are being tested on the methodology, or your ability to find solutions, then plugging-in will not do.

3/(5x) + 7/(2x) = 1

We want to multiply but stuff in various denominators, just to get rid of them, It will make life much simpler. HOWEVER, we must first make sure the denominators are NOT zero.

Domain Considerations: x != 0 Notice how x = 0 would make BOTH denominators equal to zero. We simply can't have that. So, let's just promes that x is NOT zero and proceed. If anyone tries to tell us that x = 0 is a solution, we will just smile and ignore such individuals.

3/(5x) + 7/(2x) = 1

Multiply every term by x

x*3/(5x) + x*7/(2x) = x*1
(3/5) + (7/2) = x

You could just add the fractions, now, but I'll do it a little differently.

Multiply every term by 5, just to show what might be done if the first multiplication hadn't solved ALL our problems.

5*(3/5) + 5*(7/2) = 5*x
3 + (35/2) = 5*x

Multiply every term by 2
2*3 + 2*(35/2) = 2*5*x
6 + 35 = 10*x
41 = 10*x
(41/10) = x

That is NOT the same as x = 10/41, sorry.

Now, one last thing. Check your answer in the ORIGINAL equation.

3/(5x) + 7/(2x) = 1
3/(5(41/10)) + 7/(2(41/10)) = 1 ???
3/(41/2) + 7/(41/5) = 1 ???
3*(2/41) + 7*(5/41) = 1 ???
6/41 + 35/41 = 1 ???
41/41 = 1 -- and I think we're done.

So, where did you wander off with x = 10/41?

 

[School_girl]

Well, actually I took the answer that I got in substitute it for x. And when I punched the numbers on calculator it seemed to equal 1. So, I tried like 5 times and I got 1 everytime. So, I don't know... :?