The simplified equation of [tex]\frac{x^{2}-9 }{3x^{2} +8x-3}+\frac{x-3}{x+2}[/tex] is [tex]\frac{(x-3)(4x+1)}{(3x-1)(x+2)}[/tex]
What is Simplification?
Simplification is the process of replacing a mathematical expression by an equivalent one, that is simpler. Therefore,
[tex]\frac{x^{2}-9 }{3x^{2} +8x-3}+\frac{x-3}{x+2}[/tex]
3x² + 8x - 3 = (3x - 1)(x + 3)
x² - 9 = (x - 3)(x + 3)
Therefore,
[tex]\frac{(x-3)(x+3)}{(3x-1)(x+3)} +\frac{x-3}{x+2} =\frac{(x+2)(x-3)(x+3)+(x-3)(x+3)(3x-1)}{(3x-1)(x+3)(x+2)}[/tex]
Therefore,
[tex]\frac{(x+2)(x-3)(x+3)+(x-3)(x+3)(3x-1)}{(3x-1)(x+3)(x+2)}=\frac{((x+3)(x-3)((x+2)+(3x-1)))}{(3x-1)(x+3)(x+2)}[/tex]
[tex]\frac{((x+3)(x-3)((x+2)+(3x-1)))}{(3x-1)(x+3)(x+2)}=\frac{(x-3)((x+2)+(3x-1))}{(3x-1)(x+2))}[/tex]
Therefore,
[tex]\frac{(x-3)((x+2)+(3x-1))}{(3x-1)(x+2))} = \frac{(x-3)(x+2+3x-1)}{(3x-1)(x+2)}[/tex]
[tex]\frac{(x-3)(x+2+3x-1)}{(3x-1)(x+2)}=\frac{(x-3)(4x+1)}{(3x-1)(x+2)}[/tex]
learn more on simplification here: https://brainly.com/question/24705667
