Question

Q2 Solve the equation

14/x+3 - 1 = 5/x+1
;X+-3, -1, for x.​

Answer 1

Step-by-step explanation:

(i) Solve for x over the real numbers:

-1 + 3 + 14/x = 1 + 5/x

-1 + 3 + 14/x = 2 + 14/x:

2 + 14/x = 1 + 5/x

Bring 2 + 14/x together using the common denominator x. Bring 1 + 5/x together using the common denominator x:

(2 (x + 7))/x = (x + 5)/x

Multiply both sides by x:

2 (x + 7) = x + 5

Expand out terms of the left hand side:

2 x + 14 = x + 5

Subtract x + 14 from both sides:

Answer:

x = -9

please write properly I will do (ii) again then

Answer 2

$\frac{14}{x + 3} - 1 = \frac{5}{x + 1}$

taking lcm

$\frac{14 - x - 3}{x + 3} = \frac{5}{x + 1}$

$\frac{11 - x}{x + 3} = \frac{5}{x + 1}$

cross multiply

$(11 - x)(x + 1) = 5 \times (x + 3)$

$11x + 11 - {x}^{2} - x = 5x + 15$

${x}^{2} - 5x + 4 = 0$

${x}^{2} - x - 4x + 4 = 0$

$x(x - 1) - 4(x - 1) = 0$

$(x - 1)(x - 4) = 0$

so,

$x = 1 \: or \: x = 4$