Question

Solve for all values of p: 3p/p-5 - 2/p+3 = p/p+3?

Answer 1

`p in { -1, -5}`

Explanation:

I have assume the the intended equation is:
`color(white)("XXX")color(magenta)((3p)/(p-5))-color(blue)(2/(p+3))=color(green)(p/(p+3))`
although other interpretations are possible.
Note that this equation is undefined if `p=5` or `p=-3`

`color(magenta)((3p)/(p-5) * (p+3)/(p+3))-color(blue)(2/(p+3) * (p-5)/(p-5))=color(green)(p/(p+3) * (p-5)/(p-5))`

Since the denominator is identical for all terms, we can ignore it and get:
`color(magenta)(3p(p+3))-color(blue)(2(p-5))=color(green)(p(p-5))`

`color(magenta)(3p^2+9p) -(color(blue)(2p-10))=color(green)(p^2-5p)`

`2p^2+12p+10=0`

`p^2+6p+5=0`

`(p+1)(p+5)=0color(white)("XXXX")rArr p=-1color(white)("xx")orcolor(white)("xx")p=-5`