What algebraic property can I use here?

[megaboy123]

Homework Statement

[/B]
example problem: 5 = [(x)(4+x)] / (4-x)

answer: 5

Homework Equations

Unsure what to use.

3. The Attempt at a Solution
Not sure what my professor did, but I thought that if i multiply by the reciprocal of something, I have to balance by multiplying the other side as well. It seems like everything just canceled out and the only thing left was x = 5. I would just like to know what algebraic property or technique can be used to find x BESIDES quadratic formula.

 

[Simon Bridge]

Not sure what my professor did,...

This is the purpose of taking notes in class.

... but I thought that if i multiply by the reciprocal of something, I have to balance by multiplying the other side as well.

Yes.

It seems like everything just canceled out and the only thing left was x = 5.

Do you mean that is your vague recollection of what the prof did or that is what happened when you did it?

I would just like to know what algebraic property or technique can be used to find x BESIDES quadratic formula.

...what's wrong with the usual rules for multiplication and addition?
What was the topic of the class?

Have you tried substituting the stated solution x=5 into the equation to see if it really is the solution?
(I am guessing that "answer:5 means x=5 will make the expression true...)

 

[megaboy123]

its for a general chemistry class, everything makes sense (as far as chemistry goes) up until that last step right before the answer. Not sure what you mean by rules for multiplication and addition.

 

[Simon Bridge]

I am guessing that "answer:5" means that putting x=5 into the expression 5=[x(4+x)]/(4-x) will make it true.
Have you tried this to see?

Not sure what you mean by rules for multiplication and addition.

Do you know how to add and how to multiply?

 

[Mark44]

Not sure what you mean by rules for multiplication and addition.

If you add the same quantity to both sides of an equation, the new equation will have the same solutions as the original equation.
If you multiply both sides of an equation by the same nonzero quantity, the new equation will have the same solutions as the original equation.

 

[Ray Vickson]

Homework Statement

[/B]
example problem: 5 = [(x)(4+x)] / (4-x)

answer: 5

Homework Equations

Unsure what to use.

3. The Attempt at a Solution
Not sure what my professor did, but I thought that if i multiply by the reciprocal of something, I have to balance by multiplying the other side as well. It seems like everything just canceled out and the only thing left was x = 5. I would just like to know what algebraic property or technique can be used to find x BESIDES quadratic formula.

Are you solving an equation of the form
$$
\frac{x(4+x)}{4-x} = 5 ?
$$
If so, x=5 has nothing to do with it: there are two solutions, which are obtainable from the quadratic solution formula: x ≈ -10.84 and x ≈ 1.84.