Transcript 4.6 – Solving Rational Equations

4.6 – Solving Rational Equations
“I can solve rational equations.”
Solve each equation.
Since t is a denominator –
12
+
t
–
8
=
0
t(
) *t
multiply through by t
t
You need to check to
make sure that your
12 + t2 – 8t = 0
Rearrange
terms
solutions are valid!
t2 – 8t + 12 = 0
Will either
one create a
Factor and
Solve!
(t – 6)(t – 2) = 0
t = 6 and t = 2
zero in the
denominator?
Try to solve this one!
__x__ - 2 =
20
.
x + 4 x – 1 x2 + 3x - 4 Factor to help find the
common denominator
__x__ - 2 =
20
.
x + 4 x – 1 (x + 4)(x – 1) Multiply through by
(x+4)(x-1)
20
. (x+4)(x-1)
(x+4)(x-1)( __x__ - 2 )=
x + 4 x – 1 (x + 4)(x – 1)
x(x – 1) – 2(x + 4) = 20
Simplify
x(x – 1) – 2(x + 4) = 20
Solve!
x2 – x – 2x – 8 = 20
x2 – 3x – 28 = 0
(x – 7)(x + 4)= 0
x = 7 and x = -4
Double check:
Will any solution
cause a zero in
the denominator?
Do you think you have it?
Try this one on your own!
2 + 3 = -y .
y+2 y
y+2
y = -3
4.7 – Radical Equations
“I can solve radical equations.”
“I can determine if solutions are extraneous.”
Extraneous Solutions
• Solutions that arise when solving equations,
but are not true solutions to the original
equation.
Example:
After correctly solving x = √x + 7 + 5, two
solutions were found: x = 9 and x = 2.
Check for an extraneous solution.
Solve x = √x – 3 + 3
1st move all terms not in the radical to one side, and
the radical alone on the other side.
x – 3 = √x – 3
2nd get rid of the radical
(x – 3)2 =(√x – 3)2
x2 – 6x + 9 = x – 3
x2 – 7x + 12 = 0
3rd solve! 
(x – 4)(x – 3)= 0
x = 4 and x = 3
Solve x = √x – 3 + 3
Check to see if x = 4 or 3 are extraneous!
x=4
4 = √4 – 3 + 3
4=4
x=3
3 = √3 – 3 + 3
3=3
3
Try to solve this one: 7 = 3 - √x + 11
1st move all terms not in the radical
3
to one side, and the radical alone
-4 = √x + 11
on the other side.
2nd cube both sides
(-4)3
3
= (√x + 11 )3
Simplify & Solve
-64 = x + 11
-75 = x
Changes to Assignment Guide
4.6 p247 #13 – 17 (odd), 37, 38, 46*
4.6 – due Tuesday
4.7 p255 #13, 14, 17, 38, 45, 50, 51
4.7 – due Wednesday
Quiz - Wednesday