Question

Simplify and draw ( f/g )(x) given f(x)=x²-x-2 and g(x)=x-2 .

Answer 1

To find
`\((f(x))/(g(x))\),` substitute the expressions for f(x) and g(x) into the fraction. Therefore,
`\((f(x))/(g(x))\)` becomes
`\((x^2 - x - 2)/(x - 2)\)`. This is the final simplified expression for
`\((f(x))/(g(x))\).`

`\[ (f(x))/(g(x)) = (x^2 - x - 2)/(x - 2) \]`

Step-by-step explanation:

To find
`\((f(x))/(g(x))\),` substitute the expressions for f(x) and g(x) into the fraction. Therefore,
`\((f(x))/(g(x))\)` becomes
`\((x^2 - x - 2)/(x - 2)\)`. This is the final simplified expression for
`\((f(x))/(g(x))\).`

Now, let's break down the steps for clarity. Start by substituting
`\(f(x) = x^2 - x - 2\)` and g(x) = x - ) into the fraction:

`\[ (f(x))/(g(x)) = (x^2 - x - 2)/(x - 2) \]`

To simplify this expression, factor the numerator:

`\[ ((x + 1)(x - 2))/(x - 2) \]`

Now, cancel out the common factor x - 2) in the numerator and denominator:

x + 1

So,
`\((f(x))/(g(x))\)` simplifies to x + 1. This is the simplified form of the given expression.

In summary, the simplified expression for
`\((f(x))/(g(x))\) is \(x + 1\)`. The process involves substituting the given functions into the fraction, factoring the numerator, and canceling out common factors to reach the final simplified form.