How can we solve fractional equations?

Do now: Solve for x

What steps did you use to solve?

€

x

20=

1

2

Reminders about fractions

To add or subtract we need common denominators

We can cross multiply when an equation is in the following form:

This works only if there is nothing in the equation but the two fractions.Ex. NO YES

€

2

3+

4

x=

5

6

€

2x +12

3x=

5

6

€

a

b=c

d⇒ ad = cb

So how can we actually solve

these equations?There are a few ways to do so.

One way is to cross multiply. 1) Convert the problem into nothing but fractions on either side by addition or subtraction with common denominators

2) Cross multiply 3) Solve for the variable 4) Check

ExampleFirst get common denominators so we can add.

Cross multiplySolve for x

Check

€

2x +12

3x=

5

6

€

6 2x +12( ) = 3x(5)

€

12x + 72 =15x

€

72 = 3x

€

24 = x

€

2

3+

4

x=

5

6

Is there another way to do this?

Yes, instead of rewriting everything into fractions, look for the LCD of all fractions and rational expressions

Next multiply through by this LCDNow you can solve like normalMAKE SURE YOU CHECK YOUR ANSWERS!!!

Example LCD is x2

Multiply BOTH SIDES by the LCD

Solve

Check

€

10

x 2+

3

x=1

€

x 2 10

x 2+

3

x

⎛

⎝ ⎜

⎞

⎠ ⎟=1• x 2

€

10 + 3x = x 2

€

0 = x 2 − 3x −10

€

0 = (x − 5)(x + 2)

€

x = 5, − 2

Example

€

2

y + 5+

20

y 2 − 25=1

Try on your own

€

3

a+

5

2a=

1

2

SummaryWhat are the main steps to solving these problems?

HW pg 132 1-20 even