The required simplification of rational expression is (4 + x) / (x - 3).
What is a rational number?
Any real number that can be represented in the form of p/q, where q is not equal to 0 is called a rational number. The decimal expansion of rational numbers is terminating and repeating.
Simplifying the rational expression: x² + 2x - 8 / x² - 5x + 6
Given a rational expression,
x² + 2x - 8 / x² - 5x + 6
On simplifying, we get,
For numerator, x² + 2x - 8: (x - 2)(x + 4)
For denominator, x² - 5x + 6: (x - 2)(x - 3)
Now, x² + 2x - 8 / x² - 5x + 6 = (x - 2)(4 + x) / (x - 2)(x - 3)
= (4 + x) / (x - 3)
Restriction is that the denominator, x - 3 should not be 0.
Hence, the required simplification of rational expression is (4 + x) / (x - 3)
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