Question

solve for x one upon X - 1 + 2 upon X + 2 is equal to 4 upon X + 4​

Answer 1

Answer:

x=(3/2)

Step-by-step explanation:

Here,

(x-1+2)/(x+2)=4/(x+4)

or, (x+1)/(x+2)=4/(x+4)

or,(x+1)(x+4)=4(x+2)

or,(x^2+4x+x+4)=4x+8

or, x^2+5x+4=4x+8

or,x^2+x-4=0

or,x^2+2.x.(1/2)+(1/4)=4

or,(x+(1/2))^2=2^2

or, x+(1/2)= 2

or,x= 2-(1/2)

or,x=(4-1)/2

So, x=3/2

Answer 2

Here's the Solution :

$\frac{1}{x - 1} + \frac{2}{x + 2} = \frac{4}{x + 4} \\ \\ \implies \frac{x + 2 + 2(x - 1)}{(x - 1)(x + 2)} = \frac{4}{x + 4} \\ \\ \implies \frac{x + 2 + 2x - 2}{ {x}^{2} + 2x - x - 2} = \frac{4}{x + 4} \\ \\ \implies \frac{3x}{ {x}^{2} + x - 2 } = \frac{4}{x + 4} \\ \\ \implies3x(x +4) = 4( {x}^{2} + x - 2) \\ \\ \implies3 {x}^{2} + 12x = 4 {x}^{2} + 4x - 8 \\ \\ \implies4 {x}^{2} + 4x - 8 - 3 {x}^{2} - 12x = 0 \\ \\ \implies {x}^{2} - 8x - 8 = 0$

Now by quadratic formula :

x = [-b ± √(b² - 4ac) ]/4ac

x = [ -(-8) ± √8² - 4×1×(-8) ] / 4×1×8

x = [ 8 ± √(64+32]/32

x = [ 8 ± √96] /32

x = [ 8 ± √(4²×6)]/32

x = (8 ± 4√6 ) /4×6

x =(2±√6)/6

Therefore ,

x = (2+√6)/6

And ,

x = (2-√6)/6