Add and subtract to express the following as a single ration

Add and subtract to express the following as a single rational expression. 4z/3t + 2t/t - x/3 Simplify the complex fraction Solve the rational equation Simplify the radical expression. You may assume that all variables are positive. Simplify assuming all variables are positive. Leave no negative exponents.

Solution

6. 4z/3t +2y/t -x/3

Taking Lcd as 3t:

( 4z + 6y -xt)/3t

7.   3/(x-3) / 9/(x^2 -x -6)

Take denominator : 9/(x^2 -x -6) = 9/(x^2 -3x+2x -6) = 9/(x-3)(x+2)

3/(x-3) / 9/(x^2 -x -6) = 3/(x-3) / 9/(x-3)(x+2)

= 3(x-3)(x+2)/(x-3)

= 3(x+2)

8. )   3y/4 -y/6 = 35/24

On LHS take LCD as 4*6 = 24

(3y*6 - y*4)/24 = 35/24

14y/24 = 35/24

14y = 35

y = 35/14 = 5/2

9) (48a^7b^9c^12)^1/4

48 = 2*2*2*2*3 = 2^4*3^1

Use the exponenet property: (a^x)^y = a^(xy)

So, (48a^7b^9c^12)^1/4 = (2^4*3^1a^7b^9c^12)^1/4

= (2^1)(4^3/4)(a^7/4)(b^9/4)(c^12/4)

= 2(64)^1/3b^9/4c^3