Question

5/x+3 take away 1/x-2 equals to 1. solve two possible answers for x

Answer 1

Solution:-

• First write the given equation

`\qquad{:}\longrightarrow`
`\sf \frac {5}{x+3}-(1)/(x-2)=1`

`\qquad{:}\longrightarrow`
`\sf \frac {5 (x-2)-1 (x+3)}{(x+3)(x-2)}=1`

`\qquad{:}\longrightarrow`
`\sf \frac {5x-10-x }{x^2-6x-6} =1`

• use cross multiplication method

`\qquad{:}\longrightarrow`
`\sf 5x-x-10=x^2-6x-6`

`\qquad{:}\longrightarrow`
`\sf x^2-6x-6=4x-10`

`\qquad{:}\longrightarrow`
`\sf x^2-6x-4x-6+10=0`

`\qquad{:}\longrightarrow`
`\sf x^2-10x+4=0`

• use quadratic formula

`\qquad{:}\longrightarrow`
`\sf x=\frac {-b\underline{+}\sqrt {b^2-4ac}}{2a}`

`\qquad{:}\longrightarrow`
`\sf x=\frac {10\underline{+}\sqrt {(-10)^2-4×1×4}}{2×1}`

`\qquad{:}\longrightarrow`
`\sf x=\frac {10\underline{+}√(100-16)}{2}`

`\qquad{:}\longrightarrow`
`\sf x=\frac {10\underline{+}\sqrt {84}}{2}`

`\qquad{:}\longrightarrow`
`\sf x=\frac {10+\sqrt {84}}{2}\quad or\quad x=\frac {10-√(84)}{2}`