Question

(x^2/x-3)=(x+2/2x-5)

Answer 1

Please check the explanation

Explanation:

Given the expression

`(x^2)/(x-3)=(x+2)/(2x-5)`

`\mathrm{Apply\:fraction\:cross\:multiply:\:if\:}(a)/(b)=(c)/(d)\mathrm{\:then\:}a\cdot \:d=b\cdot \:c`

`x^2\left(2x-5\right)=\left(x-3\right)\left(x+2\right)`

`2x^3-5x^2=x^2-x-6`

`2x^3-6x^2+x+6=0`

`\left(x-2\right)\left(2x^2-2x-3\right)=0`

Using the zero factor principle:

if
`ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)`

`x-2=0\quad \mathrm{or}\quad \:2x^2-2x-3=0`

so

`x-2=0`

`x=2`

and

`2x^2-2x-3=0\:\\x=(1+√(7))/(2),\:x=(1-√(7))/(2)`

so

`x=2,\:x=(1+√(7))/(2),\:x=(1-√(7))/(2)`