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).

step-by-step explanation:

two pairs of adjacent sides are of equal length. this implies that one diagonal divides the kite into congruent triangles, and so the angles between the two pairs of equal sides are equal in measure. it also implies that the diagonals are perpendicular.