Math help!! Algebra 2?

Question

1.   x/3 -1
     ----------
     x^2/3 - 3

2. find the solution set set for the equation (square root ends a 3)x^2 - 3x +3 = 1

3. solve for x: 3/x+3 + 2/x-4 = 4/3

4.If f(x) = x-2 and g(x) = x^2, find f(g(3))

5. Simplify: 3(square root) -64x^17

THANK YOU SO MUCH!!

Answer 1

3. solve for x: 3/x+3 + 2/x-4 = 4 / 3

Given equation  3 / x + 3 + 2 / x - 4  =  4 / 3

lcm of (x+3),(x-4)

 3(x-4) + 2(x+3) /(x+3)(x-4) =  4/ 3

 3x -12+ 2x + 6 / (x+3)(x-4) = 4/ 3

5x - 6  / (x+3)(x-4) = 4 / 3

5x-6 = 4/3*(x+3)(x-4)

Multiply each side by 3

 3*(5x-6) = 4/3*3*(x+3)(x-4)

15x -18  = 4(x^2-4x+3x-12)

15x -18  = 4 x^2-16x+12x-48

15x-18= 4 x^2-4x-48

4 x^2-4x-48-15x+18 = 0

4 x^2-19x-30 = 0

4 x^2-24x+5x-30 = 0

4x(x-6) +5(x-6) = 0

(x-6) (4x+5) = 0

x = 6     x = -5/4

Answer 2

4.If f(x) = x-2 and g(x) = x^2, find f(g(3))

Given f(x) = x-2 ; g(x) =x^2

 f(g(3)=f(g(3)

          =f(3^2)

          =f(9)

          =9-2

f(g(3) =7

Answer 3

3. solve for x: 3/x+3 + 2/x-4 = 4 / 3

Given equation  3 / x + 3 + 2 / x - 4  =  4 / 3

Multiply each side by x

 3(x) / x  + 3x + 2(x) / x -4(x) =  4(x) / 3

 3 + 3x + 2 -4x = 4x / 3

5 - x = 4x / 3

Multiply each side by 3

5(3) -3x =4x(3) /3

15 -3x  = 4x

Add 3x to each side 

15-3x+3x = 4x+3x

15 = 7x

x  =  15 / 7

 

Answer 4

Given equation  sqrt x^2 - 3x +3 = 1

squaring each side

(sqrt x^2 - 3x +3)^2 =1^2

x^2 - 3x +3 = 1

Subtract 1 from each side

x^2 - 3x +3-1 = 1-1

=> x^2 - 3x +2 = 0

=> x^2-2x -x +2 = 0

=> x(x-2)-1(x-2) = 0

=> (x-1) (x-2) =0

=> x-1 = 0 or x-2 = 0

=> x=1 or x=2

Answer 5

The expression is .

 

The simplified expression is 1/(x + 3).

Answer 6

5) The expression is √3 - 64x¹⁷.

Factor a minus sign out.

= -(64x¹⁷ - √3)

Substitute √3 value.

= -(64x¹⁷ - 1 .7320)

The simplified expression is -(64x¹⁷ - 1 .7320).