Definitions & Methods
When you have common factors in both the numerator and denominator, you can _________ them.
cancel
If y varies inversely as x, and y = 12 when x = 3, then what is y when x = 4?
y = 9
Simplify:
(x+10)/(5x+50)
1/5
(x^2+13x+30)/(x+1)*(x+1)/(10x+30)
(x+10)/10
(x+1)/(3x+8)+3/(3x+8)
(x+4)/(3x+8)
To add or subtract rational expressions with unlike denominators, what do you first need to find?
The LCD (least common denominator)
If y varies inversely as
x^2
and if y = 10 when x = 2, then what is y when x = 1?
y = 40
Simplify:
(10x^2-80x)/(x-8)
10x
(x^2-8x+7)/(x-7)*1/(x+2)
(x-1)/(x+2)
(5x+3)/(x-1)-(9x-1)/(x-1)
-4
What method would you use to factor this?
x^2+7x+12
Double Bubble (factoring trinomials)
Sergio can do his worksheet in 10 hours. Elijah can do the same worksheet in 8 hours. How long would it take them to complete the worksheet together?
4 hours and 27 minutes
Simplify:
(x^2+x-12)/(2(x+4))
(x-3)/2
(3x+9)/(4x^2)div(x+3)/(8x)
6/x
(2x)/(6x^2+12x)-(x-2)/(6x^2+12x)
1/(6x)
What method would you use to factor this?
16x^2-1
Difference of squares
Yory and Austin, working together, can do their Mathspace in 40 minutes. Working alone, Yory can finish the Mathspace in 1 hour. How long would it take Austin to finish it by himself?
2 hours
Simplify:
(x^2-25)/(5-x)
-(x+5)
1/(x-7)div(x-4)/(x^2-10x+24)
(x-6)/(x-7)
(5k)/(k+5)-(5k)/(k+2)
(-15k)/((k+5)(k+2))
Factor completely:
4m^2-m
m(4m-1)
Ms. Shepherd and Mr. Fox can co-teach a math lesson in 18 minutes. Ms. Shepherd can teach the lesson alone 15 minutes faster than Mr. Fox can teach it alone. How long does it take Mr. Fox to teach it alone?
45 minutes
Simplify:
(x^2+14x+40)/(5x+20)
(x+10)/5
[(x-1)/(x^2+6x-7)]/[1/(x+10)]
(x+10)/(x+7)
5/(2x-8)+(3x)/(x^2-16)
(11x+20)/(2(x-4)(x+4))