Question

50 points, question is below.

Answer 1

2

Explanation:

Given function to us is ,

`\implies f(x) =( x +5)/( x^2+3x -10)`

Here the denominator should not be equal to 0 . Therefore ,

`\implies x^2 + 3x -10 \\eq 0\\\\\implies ( x +5)(x-2) \\eq 0 \\\\\implies x \\eq 5 , -2`

We can simplify the function and write it as ,

`\implies f(x) =( x +5)/( x^2+3x -10)\\\\\implies ( ( x +5))/( ( x +5)(x-2))\\\\\implies (1)/(x-2)`

Therefore our required answer is 2 .

Answer 2

`x^2+3x-10\\eq0\\\\x^2+5x-2x-10neq0\\\\x(x-5)-2(x+5)\\eq0\\\\(x+5)(x-2)\\eq0\to x+5\\eq0\ \wedge\ x-2\\eq0\\\\x\\eq-5\ \wedge\ x\\eq2\\\\(x+5)/(x^2+3x-10)=(x+5)/((x+5)(x-2))=(1)/(x-2)\\\\Answer:\ x=2`