Answer:
a. [tex]x=-5[/tex]
Step-by-step explanation:
The discontinuity of an equation is when the denominator is equal to zero.
The denominator equation is a quadratic equation that is to say it has two possible points where x can be equal to zero (roots)
to find the roots of we use the quadratic formula
[tex]f(x)=\frac{x+5}{x^2+3x-10}[/tex]
denominator: [tex]x^2+3x-10[/tex]
[tex]a=1\\b=3\\c=-10\\ x = \frac {-b \pm \sqrt {b^2 - 4ac}}{2a}\\ x = \frac {-(3) \pm \sqrt {(3)^2 - 4(1)(-10)}}{2(1)}\\ x = \frac {-3 \pm \sqrt {9 +40}}{2}\\ x = \frac {-3 \pm \sqrt {49}}{2}\\ x = \frac {-3 \pm7}{2} \\ x_1= \frac {-3 +7}{2}\\x_1= \frac{4}{2}\\ x_1= 2\\x_2=\frac {-3 -7}{2}\\x_2= -5[/tex]
we clear the value of x from the numerator
[tex]x=-5[/tex]
Is common for both the numerator and the denominator we can cancel it and the discontinuity is removable
