1. Find the lcm of t^3 +6t^2+9t, t^2-6t?

Question

2. The officejet printer can copy Jane's dissertation in 18mins. The laserjet printer can copy the same document in 14mins. If the two machines work together how long would they take to copy the dissertation?

3. Solve. Simplify the answer
x/x+6 - 6/x-6 = x^2+36/x^2-36

4. Solve.
a) z-3/z+9=5/7
b) z+5/z = -6

5. Divide and simplify the answer
-22+11x/3 / 49x-98/9

Answer 1

t^3+6t^2+9t = t(t^2 +6t+9) = t(t+3)^2
t^2-6t = t(t-6)
So lcm is t

18*14/(18+14) = 7.875 minutes. Just take product over sum

[x(x-6)-x(x+6)]/(x^2-36) =( x^2+36)/(x^2-36)
x^2 -6x -x^2 -6x = x^2 +36
x^2+12x +36 = 0
(x+6)^2 = 0
x+6 = 0
x = -6

(z-3)/(z+9) = 5/7 Cross multiply getting:
5z +45 = 7z -21
2z= 66
z = 33

(z + 5)/z = -6
z+5 = -6z
-7z= 5
z = -5/7

(-22+11x/3)/((49x -98)/9)
= [11(-2+x)/3][9/(49(x-2))]
= -33/49

Answer 2

im just starting high school, i cant answer that