1. ## Solving Rational Expressions

Hi, I am having trouble understanding how to answer questions like this:

$\displaystyle -2= \frac {1}{5}y-1$

or

$\displaystyle \frac {-5}{2y}= \frac {1}{4}$

2. 1. Get rid of the -1 by adding 1 on bothe sides, the get rid of the x 1/5 by x5 on both sides
2. If a/b = c/d then ad=bc (called cross multiplying) then you have a simpler equation to solve

3. Originally Posted by henryW
Hi, I am having trouble understanding how to answer questions like this:

$\displaystyle -2= \frac {1}{5}y-1$

or

$\displaystyle \frac {-5}{2y}= \frac {1}{4}$
I assume you want to solve for y?

$\displaystyle -2=\frac {1}{5}y-1$

$\displaystyle -1=\frac {1}{5}y$

$\displaystyle 5\cdot(-1)=5\cdot\frac {1}{5}y$

$\displaystyle -5=\frac {5 \cdot 1}{5}y$

$\displaystyle -5= y$

For the second,

$\displaystyle \frac {-5}{2y}= \frac {1}{4}$

$\displaystyle \frac{1}{-5}\cdot\frac {-5}{2y}= \frac {1}{4}\cdot\frac{1}{-5}$

$\displaystyle \frac{1}{2y}= \frac {1}{-20}$

Take the reciprocal of both sides:

$\displaystyle 2y = -20$

$\displaystyle y = -10$

That's one way of doing it, you might not be comfortable with using reciprocals, though.

4. In general, the simplest way to handle equations with "rational fractions" is to multiply both sides by the least common denominator of all the fractions, thus elminating the fractions.

For example, to solve 3- x/5= 1/3, multiply both sides of the equation by 3(5)= 15 to get 3(15)- (x/5)(15)= (1/3)(15) or 45- 3x= 5. Then -3x= 5- 45= -40 and x= 40/3.

Warning, if your fractions have the "unknown", x, in a denominator, you must check any solutions in the original equation to see if any make a denominator 0. If so, that solution must be thrown out.