Question

Solve rational equation Please Draw Steps, and show answer please!

Answer 1

Answer:

$x=\frac{2}{5}$

Step-by-step explanation:

$\frac{2 x}{x+2}-\frac{x}{x-1}=1$

$\begin{aligned} & \Leftrightarrow \frac{2 x(x-1)}{(x+2)(x-1)}-\frac{x(x+2)}{(x-1)(x+2)}=1 \\& \Leftrightarrow \frac{2 x^{2}-2 x}{(x+2)(x-1)}-\frac{\left(x^{2}+2 x\right)}{(x+2)(x-1)}=1 \\& \Leftrightarrow \frac{2 x^{2}-2 x-\left(x^{2}+2 x\right)}{(x+2)(x-1)}=1 \\& \Leftrightarrow \frac{2 x^{2}-2 x-x^{2}-2 x}{(x+2)(x-1)}=1 \\& \Leftrightarrow \frac{x^{2}-4 x}{(x+2)(x-1)}=1 \\\end{aligned}$

$\begin{aligned}& \Leftrightarrow x^{2}-4 x=(x+2)(x-1) \\& \Leftrightarrow x^{2}-4 x=x^{2}-x+2 x-2 \\& \Leftrightarrow x^{2}-4 x=x^{2}+x-2 \\& \Leftrightarrow-4 x=x-2 \\& \Leftrightarrow 5 x=2\end{aligned}$

therefore,

$x=\frac{2}{5}$

Answer 2

$\frac{2x}{x + 2} - \frac{x}{ - 1} = 1$

$⇢ \frac{2x}{x + 2} = 1 + \frac{x}{x - 1}$

$⇢ \frac{2x}{x + 2} = \frac{(x - 1) + x}{ - 1}$

$⇢\frac{2x}{x + 2} = \frac{2x - 1}{x - 1}$

By, Cross multiplying, we get

$⇢2x(x - 1) = (2x - 1)(x + 2)$

$⇢2 {x}^{2} - 2x = 2x(x + 2) - 1( x+ 2)$

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

Here, $2 {x}^{2}$ from both sides will get cancelled

$⇢- 2x = 3x - 2$

$⇢ - 2x - 3x = - 2$

$⇢- 5x = - 2$

$⇢x = \frac{ - 2}{ - 5}$

$⇢ \underline { \boxed{ x = \frac{2}{5} }}$