Substitute yy for f(x)f(x).
y=(2x^2+5x-12)/(x+4)y=2x2+5x−12x+4
Factor the numerator using the a*ca⋅c method.
2x^2+5x-122x2+5x−12
ax^2+bx+cax2+bx+c
a=2;a=2; b=5;b=5; c=-12c=−12
a*c=2*-12=-24a⋅c=2⋅−12=−24
Find two numbers that when multiplied equal -24−24 and when added equal 55.
The numbers -3−3 and 88 fit the criteria.
Rewrite 5x5x as -3x−3x and 8x8x.
2x^2-3x+8x-122x2−3x+8x−12
Group and factor.
(2x^2-3x)+(8x-12)(2x2−3x)+(8x−12) =
x(2x-3)+4(2x-3)x(2x−3)+4(2x−3) =
(x+4)(2x-3)(x+4)(2x−3)
Rewrite the numerator as (x+4)(2x-3)(x+4)(2x−3).
y=((x+4)(2x-3))/(x+4)y=(x+4)(2x−3)x+4
Cancel (x+4)(x+4).
y=(cancel(x+4)(2x-3))/cancel(x+4) =
y=2x-3
Make a table of x and y. Plot the points, and draw a line through the points.
Table of x and y values.
x=-2; y=-7
x=0; y=-3
x=2; y=1
graph{y=2x-3 [-11.3, 11.2, -7.56, 3.69]}
