Page 609 - Algebra 1

Example
3
___
Subtracting with Unlike Denominators
Subtract. Simplify your answers.
x+3- __
x - 4 x2 + x - 20 SOLUTION
x+3- __
x - 4 x2 + x - 20 = x + 3 - 2
2 _
2 _
Factor the denominators.
Write each expression using the LCD.
Multiply.
Subtract.
(x - 4)(x + 5)
The numerator cannot be factored; the expression is in simplified form.
Simplifying with Opposite Denominators
Add. Simplify your answer.
8 +v-7 __
v-4 4-v SOLUTION
The denominators are opposites. Multiplying either denominator by -1 will make both denominators the same.
x-4 _
(x - 4)(x + 5)
x+5 2 ___
= x + 3 ( )- x-4 x+5
(x-4)(x+5) =x2+8x+15 - 2
____ (x - 4)(x + 5) (x - 4)(x + 5)
= x2 + 8x + 13 __
Example
4
8 +v-7 __
v-4 4-v
8 _-1 v-7
__ = v - 4 (-1 )+ 4 - v
Multiply the numerator and denominator by -1. Simplify.
Add numerators.
Combine like terms.
= -8 + v-7 __
4-v 4-v = -8 + v - 7
__ _4 - v
= v - 15 4-v
Example
5
Application: Transportation
Hint
A plane flying into a headwind is going against the wind, and is therefore slower. A plane with a tailwind is flying with the wind, and is therefore faster.
594 Saxon Algebra 1
A plane flies 2000 miles with a headwind and makes the return trip
with a tailwind. Write and simplify an expression for the total time of
the round-trip flight assuming that the wind speed w remains constant and the plane’s rate averages 500 miles per hour.