6a to the 4th power/5p to the fourth power * 25p to the 7th power/36a Multiply and
Simplify
6a 4 25 p 7 5 3 3
"
= a p
5 p 4 36a 6
! 5/y divide 45/y Divide and simplify
5 45 5 y
5 1
÷
= "
=
=
y y
y 45 45 9
! t+u/tu² + 8t+u/t²u (simplify and answer)
t + u 8t + u t 2 + tu 8tu + u 2 t 2 + tu + 8tu + u 2 t 2 + 9tu + u 2
+ 2 = 2 2 + 2 2 =
=
tu 2
t u
t u
t u
t 2u2
t 2u2
! z-7/z - 9z-14/11z Simplify answer
z " 7 9z "14 11( z " 7) 9z "14 11z " 77 " 9z +14 2z " 63
"
=
"
=
=
z
11z
11z
11z
11z
11z
! 11(x-7) and 77(x-7) find the lcm
LCM = 77(x-7)
Simplify by removing factors of 1. q²-4/(q+2)²
q2 " 4
(q + 2)
2
! x-8/x-9 = 1/x-9
=
(q " 2)(q + 2) = (q " 2)
(q + 2)(q + 2) (q + 2)
solution is x=
There is no solution.
The speed of a train A is 6mph slower than the speed of train B. Train A travels 200
miles in the same it takes train B to travel 230 miles. Find the speed of each train.
Train B = 46 mph
Train A = 40 mph
s/7-7/s=0 Solve. What are the solutions.
s = 7, -7
x²+13x/x²-2x + x²-8x/x²-2x Add. Simplify
x 2 "13x x 2 " 8x 2x 2 " 21x x (2x " 21) 2x " 21
+
= 2
=
=
x 2 " 2x x 2 " 2x
x " 2x
x ( x " 2)
x "2
! Jack usually mows his lawn in 5 hours. Marilyn can mow the same yard in 7 hours. How
much time would it take for them to mow the lawn together.
2
11
hours
12
! 7/y-4 – 7/4-y Subtract. Simplify, if possible
14
y "4
! Find all numbers for which the rational express is undefined. -17/22w
Undefined for w = 0
Find the LCM z³+10z²+25z,z²-10z
z(z + 5)2(z – 10)
16.Simplify by removing factors of 1.
35z to the 9th power/42z to the 8th power
35z 9 5
= z
42z 8 6
! 17. z/14-z/35=1/14 Solve.
z = 5/3
18. x/x+8 – 8/x-8 = x²+64/x²-64 Solve.
There is no solution. (Any chance that there is a typo in the problem?)
19. 49h/7h-49 + 8h/49h-343=
351h
49h " 343
! 20. z²-16/z divided by z-4/z+3 Divide and Simplify
(z + 4 )( z + 3)
z
! 21. 1/w+2 + 2/7w Add.
9w + 4
7w ( w + 2)
! 22. Simplify by removing factors of 1. 3n²+3n/6n²+9n
n +1
2n + 3
! 23. h+9/h-2 divided by 4h+36/h-7
h"7
4 ( h " 2)
!