Can you help? Solve h - 2/h - 3 = 1/-f for h.

[d2mitch]

Found this practice problem via a google search. The website only gave the problem and the answer. I am unable to get the answer the website gives. Thank you for any help you can give!


h - 2/h - 3 = 1/-f

Solve for h.


Answer given: h = 2f + 3/f + 1​

 

[ksdhart2]

The first thing I note is that you definitely need to use grouping symbols. As you've written the problem, it would literally be interpreted as:

\(\displaystyle h-\dfrac{2}{h}-3=\dfrac{1}{-f}\)

I know that's not what you meant because the solution to that is a very very ugly expression that's not even close to the solution you posted. I'll assume that instead you meant (h-2)/(h-3)=1/-f or:

\(\displaystyle \dfrac{h-2}{h-3}=\dfrac{1}{-f}\)

That equation, solved for h does give the desired solution, namely:

\(\displaystyle h=\dfrac{2f+3}{f+1}\)

Now, that aside, you say you're unable to get the same answer as the website. That implies you've made (at least one) attempt at this problem. Please share with us any and all work you've done on this problem, even the parts that you know for sure are wrong. Thank you.

 

[d2mitch]

You're exactly right in your assumption. Thank you for pointing out my oversight. I had originally typed the problem as you did in your second example. However, when I attempted to preview my post, the problem appeared completely out of order. Thus, I quickly re-entered it in a different format, completely forgetting grouping symbols.

All that said, if anyone could help me figure out what steps to take to solve this problem, I'd be grateful. Thank you so much.

 

[Steven G]

You're exactly right in your assumption. Thank you for pointing out my oversight. I had originally typed the problem as you did in your second example. However, when I attempted to preview my post, the problem appeared completely out of order. Thus, I quickly re-entered it in a different format, completely forgetting grouping symbols.

All that said, if anyone could help me figure out what steps to take to solve this problem, I'd be grateful. Thank you so much.

Yes, someone will help you out. But first, as already pointed out, you need to tell us where you are stuck. What have you tried?

 

[Harry_the_cat]

The first thing I note is that you definitely need to use grouping symbols. As you've written the problem, it would literally be interpreted as:

\(\displaystyle h-\dfrac{2}{h}-3=\dfrac{1}{-f}\)

I know that's not what you meant because the solution to that is a very very ugly expression that's not even close to the solution you posted. I'll assume that instead you meant (h-2)/(h-3)=1/-f or:

\(\displaystyle \dfrac{h-2}{h-3}=\dfrac{1}{-f}\)

That equation, solved for h does give the desired solution, namely:

\(\displaystyle h=\dfrac{2f+3}{f+1}\)

Now, that aside, you say you're unable to get the same answer as the website. That implies you've made (at least one) attempt at this problem. Please share with us any and all work you've done on this problem, even the parts that you know for sure are wrong. Thank you.

A hint: If\(\displaystyle \frac{a}{b} =\frac{c}{d}\) then \(\displaystyle a*d = b*c\). This is called "cross-multiplying".

 

[d2mitch]

Ok, you'll have to bear with me, as every time I preview my post, everything has been rearranged. To reduce the chance of this continuing, I'll just type out, "long-hand," if you will, the steps I've done.