I need help with this!!

Question

Does anyone know how to solve this problem using the FHRATEY method?

F: Factor

Factor numerator and denominator. Cross out any that are the same in the numerator and denominator.

H: Holes

Make sure to plug them in to find the y value.

R: Roots

Make numerator equal to zero and solve

A: Vertical Asymptote

Make denominator equal zero

T: Togetherness

Only for denominator, even exponent means together, odd exponent is apart

E: End Behavior

If dN > dD of the numerator, the HA is zero.

If dN = dD then HA = lN/lD (leading coefficients)

Y: Y Intercepts

Make all x's equal zero and solve.

The problem is this f(x)=5(x+4)/x^2+x-12

Answer 1

For

f(x) = 5(x+4)/x² + x - 12

Factor

The numerator needs no further factoring

The denominator does need factoring

Denominator Factors as follows:

(x + 4)(x - 3)

f(x) simplifies to

5(x + 4)/(x + 4)(x - 3)

Canceling

the factor (x + 4) is in the numerator and denominator so it can be canceled, crossed out.

f(x) simplifies further to

f(x) = 5/(x -3)

You can't have division by 0, therefore, x cannot equal positive 3

f(x) = 5/-3 when x is zero

Remember you can graph your function at Desmos.com as y = 5/(x - 3). Note positive 3 is a barrier or asymptote. The x axis is also a barrier.

I hope this helps.