Rational Equations... I don't get them. How do you do these?

Question

1.

X-3

_____ =

X-5




3
___
X-5












2.

X-6 =



-9
_____
X









3.

b-5
____ =

b-3




b-5
____
3













4.


n
_______ =

n+2





n
___

2n

Answer 1

Solve rational equations by eliminating the denominator. Question 1 can be solved by multiplying both sides of equation by (x-5)/1

This cancels denominator so that you are left with x-3 = 3

Question 2 can be solved by multiplying both sides by x/1
Question 3 by multiplying both sides by (3)(b-3)
Question 4 by multiplying both sides by (2n)(n+2)

Then solve for your variable.

Answer 2

i'm not gonan do your homework for you, but i'll show you how to solve the first one just as an example.

In these types of problems what you want to do is get rid of the denominators by multiplying each side by all the present denominators, so for the first one multuply both sides by (x-5), the (x-5) cancels and you are left with x-3=3

for the other problems you may have to multiply both sides by more than one term, like in the last one you have to multiply both sides by (n+2) and by (2n)

Answer 3

1. (x-3)/(x-5)=3/(x-5) , x is not equal to 5 because you can't divide by 0. Multiply both sides by (x-5) to get

x-3 = 3 so your solution is x = 6

2. x-6 = -9/x x not equal to 0. This one you multiply both sides by x to get
(x-6)x = -9
x^2 -6x +9 = 0
(x-3)(x-3)=0 so the only solution is x = 3

3. multiply both sides by 1/(b-5) to get
1/(b-3) = 1/3 so b-3=3, b =6

4. is similar, multiply both sides by 1/n.
n+2 = 2n
n = 2
hope this helps

Answer 4

You need to clear the denominators.