This week in precalculus 11, we learned about rational expressions. We learned how to multiply and divide them, add and subtract them, and how to solve them completely. In this post, I will be focusing on the solving aspect.
Note that the equations could result in a linear or quadratic equations and that there are restrictions.
Ex.
The first step is to see if the fractions can factor out.
The next step is to evaluate if you have to multiply by a common denominator or cross multiply.
In this case, we cannot cross multiply since there are 3 expressions, 2 on one side of the equal sign and one on the other, which means that we have to use the multiplying by a common denominator method. you have to multiply the top and bottom of the fractions by the same number(s)/expression(s) (common denominator) and when you multiply the denominator by the same expression, it cancels out.
Common denominator: (x-4)(x+4)
+
= 
(x-4)(x+4)
+ (x+4)
= (x-4)(x+4)
Once the expressions are canceld out, multiply the numerator by the remaining expression, if there is one.
(x+4) + 2(x-4) = 5
From here, you expand, add or subtract like terms, then solve.
x + 4 + 2x – 8 = 5
3x -4 = 5
3x = 9
x = 3
State the non-permissable values.
x ≠ 4, -4