Solving Rational Equations: 3y/3y+9 + 8y+16/2y+6 = y-4/y+3

BTW i get y = -3 which creates 0 for one denominator making it NO SOLUTION
 
This is basic algebra.

The kinds of rules that we have been discussing are generalizations about numbers. If you don't understand a mechanical rule, try it with numbers (generally not 0 or 1 because they have some special properties.

\(\displaystyle \dfrac{6 + 2}{2} = \dfrac{8}{2} = 4.\) Agree?

\(\displaystyle \dfrac{6 + 2}{2} = \dfrac{6 + 1}{1} = 7.\) WRONG, WRONG, WRONG.

\(\displaystyle \dfrac{6 + 2}{2} = \dfrac{2(3 + 1)}{2} = \dfrac{3 + 1}{1} = 4.\) Perfectly OK.

A rule of algebra is

\(\displaystyle \dfrac{ab + ac}{ad + ae} \equiv \dfrac{a(b + c)}{a(d + e)} \equiv \dfrac{b + c}{d + e}.\)

If you study foundations of mathematics, you can prove that rule. But if you want to understand why it works, do some examples.
 
Interesting, Thanks Denis. That is an imagination for my figment.


No solution was the actual answer that MyMathLab wanted. (we use MyMathLab for the course I'm taking)
I already knew the destination I just wanted to know how to get there.


I like how everybody pitches in on this forum. You get a lot of different but valuable ways of approaching things.
 
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\[\frac{x+1}{x+7}=\frac{x^{2}-51x}{x^{2}+5x-14}-\frac{x-7}{x-2}\]

How do you left align this?
 
\(\displaystyle \frac{x+1}{x+7}=\frac{x^{2}-51x}{x^{2}+5x-14}-\frac{x-7}{x-2}\)

Hit reply with quote to see how I did it. You invoke LaTeX best on this site using tex and /tex in square brackets as delimiters.
 
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