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May 22nd

May 22nd

# Solving Rational Equations

I. Formulas /solving-literal-equations-for.html">Literal Equations & Formulas
A. A literal equation is an equation with more than one variable .
B. A formula is a literal equation ex pressing an application .

II. Solving Literal Equations
A. Procedure

1. Isolate the term that contains the variable that you wish to solve for by using

2. Isolate the variable that you wish to solve for by using the Multiplication
Property.

B. Examples - Solve for the specified variable.

1. I = prt; Solve for r
The variable term that contains the variable that we want to solve for is
already isolated on the right side, so we can move on to the next step . We
isolate the r on the right side by dividing both sides by pt:

2. P = a + b + c; Solve for b
We will subtract both a & c from both sides to isolate b on the right:
P − a − c = a − a + b + c − c
OR

Answer: b = P − a − c

3. Ax + By = C; Solve for y
We begin by subtracting Ax from both sides to isolate the By term:
Ax − Ax + By = C − Ax
OR
By = C − Ax
Now we divide both sides by B to isolate y on the left side:

4. Now you try one: A = p + prt; Solve for r

5. Solve for R.

Even though this is a literal equation, we still approach it the same way. We
begin by multiplying both sides by the LCD :

S(1 − R) = A − RL
Now we distribute on the left side:

S − SR = A − RL
We now need to get all the terms with "R" in them on one side. Let's do that
by adding RL to both sides:

S + RL − SR = A
Now we need to get all the "R" terms isolated on the left side by subtracting S
from both sides:

RL − SR = A − S
We notice that R is the GCF on the left , so we factor it out to get:

R(L − S) = A − S
Now divide both sides by what R is multiplied by, (L − S):

6. Now you try one: Solve for z.

7. Solve for a.

First, we need to clear the fractions by multiplying both sides by the LCD, in
this case that is a(a − c). We get:

ab = d(a − c) Distribute
ab = ad − dc Subtract ad from both sides to get all the "a" terms together.
ab − ad = −dc Factor out the GCF on the left side.
a(b − d) = −dc Divided both sides by (b - d) to isolate a.