[MOVED] need help solving (3x-25)/(x+7) - 5 = 3/x

[notamathwiz21]

Alright, I had a math problem on my Pre-Calc quiz today and I cannot figure it out. My teacher did not state whether or not it could be solved so I am kind of thinking it is a trick question. I have tried multiplying by the recipracol and I cannot solve for x. Here is the equation:

Solve for x.

3x-25 3
_____ -5 = _____
x+7 x

However, I am begining to think you cannot. My teacher is giving us 10 minutes tomorrow to finish the quiz. HELLLLLP!! Please, if you have any idea on how to help me.

 

[galactus]

What is that supposed to be?.

Is this it: \(\displaystyle \frac{3x-5}{x+7}-5=\frac{3}{x}\)

 

[notamathwiz21]

yes, sorry. i don't know how to type these things in.

 

[stapel]

i don't know how to type these things in.

To format, use LaTeX (as the tutor did, in his reply) or standard single-line formatting, as:

. . . . .(3x - 5) / (x + 7) - 5 = 3 / x

You can learn more about formatting by following the links in the "Forum Help" pull-down menu at the very top of this page.

By the way, I'm not sure what you mean by "solving by reciprocals"...? A good first step for solving a rational equation would be to multiply through by the common denominator, thus clearing all of the fractions.

If you get stuck, please reply showing your steps. Thank you.

Eliz.

 

[galactus]

You must use

 when you type in the way you did.

Better yet, learn LaTex. You can click on quote in my post to see the code I used.

Anyway, back to the problem. Yes, it can be solved.

[tex]\L\\\frac{3x-25}{x+7}-5=\frac{3}{x}[/tex]

Find the LCD, which is [tex]\L\\x(x+7)[/tex]

[tex]\L\\x(\sout{x+7})\frac{3x-25}{\sout{x+7}}-x(x+7)5=\sout{x}(x+7)\frac{3}{\sout{x}}[/tex]

This gives: [tex]\L\\-2x^{2}-60x=3x+21[/tex]

[tex]\L\\-2x^{2}-63x-21=0[/tex]

Solve the quadratic.

 

[notamathwiz21]

Why is the LCD x(x+7)? I understand how to use it, is it just because there is the x on the one side and the x+7 on the other?

 

[stapel]

Why is the LCD x(x+7)?

You have two denominators: x + 7 and x. What else would the Least Common Denominator be, but "x(x + 7)"?

Eliz.

 

[notamathwiz21]

Just making sure I understood.

 

[Denis]

In case this helps; just another way (my favorite!)

(3x - 5) / (x + 7) - 5 = 3 / x
Move the 5:
(3x - 5) / (x + 7) = 3 / x + 5
Complete right side:
(3x - 5) / (x + 7) = (3 + 5x) / x
Crisscross multiplication:
5x^2 + 38x + 21 = 3x^2 - 25x
2x^2 + 63x + 21 = 0

OK?