Page 626 - Algebra 1

Example
4
SOLUTION
__1
x
1 - _1 x
Combining Fractions to Simplify
_1 Simplify _x .
1 - _1 x
Hint
Find the LCD of
1 and _1 to subtract in
the denominator.
x
__1 = _x
Subtract in the denominator.
Write using a division symbol. Multiply by the reciprocal.
Divide out common factors. Simplify.
x-1 x_
= _1 ÷ x_
= _1 · x_
= _1 · x - 1 _x
x-1
x x
x-1 x
1 =x-1
Example 5_Application:SpeedWalking
3x2 - 12x
t took Max minutes to speed walk to the gym that was
I_
5x - 20 3x
x3 miles away. Find his rate in miles per minute.
SOLUTION
Hint
Use the formula d = rt.
_d r=t_
Solve for r. _5 x - 2 0
x3 __
r= 3x2-12x
= 5x-20 ÷ 3x2 -12x
Evaluate for d and t.
Write using a division symbol. Multiply by the reciprocal.
Factor out any GCFs.
Divide out common factors and simplify.
_3x _ x3 3x
= 5x - 20 · 3x __
x3 3x2 - 12x = 5(x - 4) · 3x
__
x3 3x(x - 4)
=_5 milesperminute x3
Theexpression_5 representsMax’sspeed-walkingrateinmilesperminute. x3
Lesson 92 611