Question

9/x+2=x+3/x-5 Can someone solve for me with steps?

Answer 1

`\\ \tt\longmapsto (9)/(x+2)=(x+3)/(x-5)`

`\\ \tt\longmapsto 9(x-5)=(x+2)(x+3)`

`\\ \tt\longmapsto 9x-45=x^2+5x+6`

`\\ \tt\longmapsto x^2-4x+51=0`

• a=1
• b=-4
• c=51

Let's find x

`\\ \tt\hookrightarrow x=(-b\pm √(b^2-4ac))/(2a)`

`\\ \tt\hookrightarrow x=(4\pm√(16-204))/(2)`

`\\ \tt\hookrightarrow x=(4\pm √(-188))/(2)`

`\\ \tt\hookrightarrow x=(4\pm √(188)i)/(2)`

• i=√-1

`\\ \tt\hookrightarrow x=(4\pm 2√(47)i)/(2)`

`\\ \tt\hookrightarrow x=2\pm √(47)i`