1. solve the rational equation quantity 4 times x plus 3 end quantity divided by 5 equals quantity 8 times x minus 1 end quantity divided by 9.

x = 0.5

x = 2

x = 8

x = 9

2. determine the vertical asymptote for the rational function f of x equals quantity x minus 4 end quantity divided by quantity 2 times x plus 3 end quantity.

x = −4
x equals negative three halves
x equals three halves
x = 4

1. x = 8

2.

Step-by-step explanation:

1. Solve the rational equation

First, cross multiply:

Now, use distributive property:

Separate terms with x and without x into different sides of equation:

Simplify:

Divide by -4:

2. The rational function

This rational function is undefined for all values of x, for which the denominator is equal to 0. Find these values:

This means that the line is a vertical asymptote for the rational function f(x).

a)(x-2)^2+(y-1)^2=9

step-by-step explanation:

(picture explains)