This week in precalc 11, we finished our whole unit on rational expressions and equations. One of my favorite things we learned was solving rational equations.

There are many different ways you can solve a rational equation such as moving the terms to one side, cross multiplying, multiply each fraction by a common denominator, etc. Whatever question you are presented with, you must choose the best option so you can solve your question efficiently.

Here is one way to solve an equation with cross multiplying : $\frac{5}{x+1} = \frac{2}{x+2}$

Since it is called cross multiplying you take whatever is on the top left term and the bottom right term then combine together (only allowed to cross multiply when an = sign is between two terms), then proceed to do the same with the rest which will give us this $5(x+2) = 2(x+1)$

Now we finish this question off with basic algebra, you distribute then solve for x !

$5x +10 = 2x +2$

$3x = -8$

$x = -\frac{8}{3}$

Another way to solve is by multiplying each fraction by a common denominator $\frac{5}{x} + 2 = \frac{3}{x}$

For this equation, we know that the common denominator is x so we can multiply everything by x

Since there is an x on the top and the bottom for 2 of the 3 terms, you can cancel them out because one number divided by the same number = 1

It will leave us with $5 + 2x = 3$, we can now solve algebraically as usual

$2x = -2$

$x = -1$

As for the more complicated questions with quadratics, we must know how to factor then find the common denominators. Solving is fairly simple as long as you do not mess up the first few steps, after then its all algebra that we have been doing since middle school.