Explanation

(12x + 8)/(x(x + 4)) = A/x + B/(x + 4)

Multiply both sides by x(x + 4):

12x + 8 = A(x + 4) + B(x)

Put x = 0:

12(0) + 8 = A(0 + 4) + B(0)

8 = 4A

A = 2

Put x = -4:

12(-4) + 8 = A(-4 + 4) + B(-4)

-48 + 8 = -4B

-40 = -4B

B = 10

Therefore:

(12x + 8)/(x(x + 4)) = 2/x + 10/(x + 4)

Last verified on 25-05-2026

Explanation

f(x) = x² - 4x

f(4) = 4² - 4(4) = 16 - 16 = 0  

f(2) = 2² - 4(2) = 4 - 8 = -4  

f(4) - f(2) = 0 - (-4) = 4

Last verified on 25-05-2026

Explanation

Since y ∝ x³, we have y = kx³ for some constant k.

1. Find k using y = 54 when x = 3:  

54 = k(3³) = k(27)  

k = 54 / 27 = 2

2. Now find y when x = 2:  

y = 2(2³) = 2(8) = 16

Last verified on 25-05-2026

Explanation

(3x + 2)/4 = (x + 6)/2

Multiply both sides by 4:

3x + 2 = 2(x + 6)

Expand RHS:

3x + 2 = 2x + 12

Collect x terms:

3x - 2x = 12 - 2

x = 10

Last verified on 25-05-2026

Explanation

Original: x² - 10x + 21 = 0  

Substitute x → x + 1:

(x + 1)² - 10(x + 1) + 21 = 0  

x² + 2x + 1 - 10x - 10 + 21 = 0  

x² - 8x + 12 = 0

Last verified on 25-05-2026