Question

Simplity. State the result in simplest fort (2x+10)/(x²+x-2)+(2)/(x+2)+(x)/(x-1),x!=-2,1

Answer 1

To simplify the expression (2x+10)/(x²+x-2)+(2)/(x+2)+(x)/(x-1), we first find the common denominator, combine the fractions, and then simplify to get the result in its simplest form.

Step-by-step explanation:

The student is asking for help with simplifying a complex rational expression: (2x+10)/(x²+x-2)+(2)/(x+2)+(x)/(x-1), given that x ≠ -2, 1. To simplify this expression, we need to find a common denominator, combine the fractions, and then simplify the resulting expression.

Simplifying Step-by-Step

1. Factor the quadratic denominator in the first term: x² + x - 2 can be factored into (x + 2)(x - 1).
2. Notice that the other denominators are (x + 2) and (x - 1), which are already part of the factored quadratic. Thus, the common denominator is (x + 2)(x - 1).
3. Write each term with the common denominator, combine them, and simplify. Ensure that terms are cancelled where applicable and the expression is reduced to its simplest form.

After following these steps, the student will have the expression in its simplest form, assuming no mistakes are made during the simplification process.