Me answer this maths question.☺***must show step by step guide to how you got your answers***☺

(i) y = k/(k + w); k = 1/2; w = 1/3

y = (1/2)/(1/2 + 1/3)

y = (1/2)/(3/6 + 2/6)

y = (1/2)/5/6)

y = 1/2 * 6/5

y = 6/10

y = 3/5

(ii) x/(x - 1) - 1 =

= x/(x - 1) - (x - 1)/(x - 1)

= [x - (x - 1)]/(x - 1)

= (x - x + 1)/(x - 1)

= 1/(x - 1)

(iii) 4^(2x + 1) = sqrt(8)

4 = 2^2, and 8 = 2^3

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

2^(4x + 2) = (2^(3))^(1/2)

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

4x + 2 = 3/2

4x = 3/2 - 2

4x = -1/2

x = -1/8

(iv) x - 3 = sqrt(3x - 11)

Square both sides.

(x - 3)^2 = ( sqrt(3x - 11) )^2

x^2 - 6x + 9 = 3x - 11

x^2 - 9x + 20 = 0

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

x = 4 or x = 5

Check:

For x = 4

x - 3 = sqrt(3x - 11)

4 - 3 = sqrt(3 * 4 - 11)

1 = sqrt(12 - 11)

1 = sqrt(1)

1 = 1

1 = 1 is a true statement, so x = 4 is a valid solution.

For x = 5

x - 3 = sqrt(3x - 11)

5 - 3 = sqrt(3 * 5 - 11)

2 = sqrt(15 - 11)

2 = sqrt(4)

2 = 2

2 = 2 is a true statement, so x = 5 is a valid solution.