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abidemiokin

The simplified form of the function is [tex]f(x) = \frac{x+3}{x}[/tex]

Functions and equation

Given the following function as shown:

[tex]f(x)=\frac{x^2-9}{x^2-3x}[/tex]

This can be factorized as:

[tex]f(x)=\frac{x^2-3^2}{x(x-3)}\\f(x)= \frac{(x+3)(x-3)}{x(x-3)} \\[/tex]

Cancel out the common terms:

[tex]f(x) = \frac{x+3}{x}[/tex]

Hence the simplified form of the function is [tex]f(x) = \frac{x+3}{x}[/tex]\

Learn more on functions here: https://brainly.com/question/10439235

Itz5151

Hi Phoenix! :)

I'm much late lol.

Answer:

[tex]\boxed{ \cfrac{x + 3}{x}} [/tex]

Step-by-step explanation:

Given:

[tex] \cfrac{x {}^{2} - 9}{x {}^{2} - 3x } [/tex]

Solution:

[Here the best option is to factorise the expression.]

Rewrite the numerator of the expression as

[tex] \cfrac{x {}^{2} - 3 {}^{2} }{x {}^{2} - 3x} [/tex]

It can be seen that the numerator is like an algebraic identity:

> a² - b² = (a+b)(a-b)

ATP, numerator : a = x² and b = 3²

  • [tex] \cfrac{(x + 3)(x - 3)}{ {x}^{2} - 3x} [/tex]

Now in the denominator take x common:

  • [tex] \cfrac{(x + 3)(x - 3)}{x(x - 3)} [/tex]

(x-3) in the denominator and (x-3) in the numerator gets canceled.

  • [tex] \cfrac{(x + 3) \cancel{(x - 3)}}{x \cancel{(x - 3)}} [/tex]
  • [tex] \boxed{\cfrac{x + 3}{x} }[/tex]

Welp,Done, that's it! :D

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