Question

1/x+3 - 1/ x- 8 = 11/33; x not equal to -3 8

Answer 1

Answer:

x = 2 or 3

Step-by-step explanation:

Hi,

Given that 1/(x + 3) - 1/(x - 8) = 11/30

Taking L.C.M, we get

[(x - 8) - (x + 3)]/(x + 3)(x - 8) = 11/30

-11/(x + 3)(x - 8) = 11/30

On cross multiplying by 30(x + 3)(x - 8)/11 on both sides, we get

-30 = (x + 3)(x - 8)

x² -8x + 3x - 24 = -30

x² - 5x + 6 = 0

(x - 2)(x - 3) = 0

x = 2 or x = 3

Hope, it helps !

Answer 2

Answer:

Step-by-step explanation:

Given equation is

$\frac{1}{(x+3)}-\frac{1}{(x-8)}=\frac{11}{33}$

Find the value of x

$\frac{1}{(x+3)}-\frac{1}{(x-8)}=\frac{11}{33}\\\\\Rightarrow\frac{(x-8)-(x+3)}{(x+3)(x-8)}=\frac{1}{3}\text{ LCM of (x+3) and (x-8) are (x+3)(x-8)}\\\\\Rightarrow\frac{x-8-x-3}{(x+3)(x-8)}=\frac{1}{3}\\\\\Rightarrow\frac{-11}{(x+3)(x-8)}=\frac{1}{3}\\\\\Rightarrow(x+3)(x-8)=-33\\\\\Rightarrow(x^{2}-8x+3x-24)=-33\\\\\Rightarrow{x}^{2}-5x-24+33=0$

$\Rightarrow{x}^{2}-5x+9=0$ ........ equation-1

For Quadratic Equation $ax^{2}+bx+c=0 \text{ [where x is the variable and a, b and c are known values]}$

the value of $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$

$b^{2}-4ac \text{ is called Discriminant (D)}$

when Discriminant (D) is positive, we get two Real solutions  for x

when Discriminant (D) is zero we get just ONE real solution (both answers are the same)

when Discriminant (D) is negative we get a pair of Complex solutions

In equation 1 the Discriminant (D) is = $b^{2}-4ac= {(-5)}^{2}-4\times1\times9=25-36=-9$

As the Discriminant (D) is negative, we get a pair of Complex solutions for x

A Complex Number is a combination of a  real number and an imaginary number

therefore the value of x is either $x=\frac{-b+\sqrt{D}}{2a}\text{or}\text{ } x=\frac{-b-\sqrt{D}}{2a}$

$x=\frac{-b+\sqrt{D}}{2a}=\frac{-(-5)+\sqrt{-9}}{2}=\frac{5+3i}{2}$

$x=\frac{-b-\sqrt{D}}{2a}=\frac{-(-5)-\sqrt{-9}}{2}=\frac{5-3i}{2}$