Question

Solve rational equation

Please Draw Steps, and show answer please!

Answer 1

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

`⇢ (2x)/(x + 2) = 1 + (x)/(x - 1)`

`⇢ (2x)/(x + 2) = ((x - 1) + x)/( - 1)`

`⇢(2x)/(x + 2) = (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 = ( - 2)/( - 5)`

`⇢ \underline { \boxed{ x = (2)/(5) }}`

Answer 2

`x=(2)/(5)`

Explanation:

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

`\begin{aligned} & \Leftrightarrow (2 x(x-1))/((x+2)(x-1))-(x(x+2))/((x-1)(x+2))=1 \\& \Leftrightarrow (2 x^(2)-2 x)/((x+2)(x-1))-(\left(x^(2)+2 x\right))/((x+2)(x-1))=1 \\& \Leftrightarrow (2 x^(2)-2 x-\left(x^(2)+2 x\right))/((x+2)(x-1))=1 \\& \Leftrightarrow (2 x^(2)-2 x-x^(2)-2 x)/((x+2)(x-1))=1 \\& \Leftrightarrow (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=(2)/(5)`