Question

1/x+2+1/x=3/4
plz solve this
​

Answer 1

Answer:

x=-4/3 or x= 2

Step-by-step explanation:

$\frac{1}{x + 2} + \frac{1}{x} = \frac{3}{4}$

$= \frac{x + x + 2}{ {x}^{2} + 2x } = \frac{3}{4} \ \\ = \frac{2(x + 1)}{ {x}^{2} + 2x} = \frac{3}{4}$

$8x + 8 = 3 {x}^{2} + 6x$

$2x + 8 = 3 {x}^{2}$

$3 {x}^{2} - 2x - 8 = 0$

$3 {x}^{2} - 6x + 4x - 8$

$3x(x - 2) + 4(x - 2) = 0$

$(3x + 4)(x - 2) = 0$

=> x= -4/3 or x= 2

Answer 2

x+2

1

+

x

1

=

4

3

\begin{gathered}= \frac{x + x + 2}{ {x}^{2} + 2x } = \frac{3}{4} \ \\ = \frac{2(x + 1)}{ {x}^{2} + 2x} = \frac{3}{4}\end{gathered}

=

x

2

+2x

x+x+2

=

4

3

=

x

2

+2x

2(x+1)

=

4

3

8x + 8 = 3 {x}^{2} + 6x8x+8=3x

2

+6x

2x + 8 = 3 {x}^{2}2x+8=3x

2

3 {x}^{2} - 2x - 8 = 03x

2

−2x−8=0

3 {x}^{2} - 6x + 4x - 83x

2

−6x+4x−8

3x(x - 2) + 4(x - 2) = 03x(x−2)+4(x−2)=0

(3x + 4)(x - 2) = 0(3x+4)(x−2)=0

=> x= -4/3 or x= 2