The right answer is C. never
The quotient of two algebraic expressions is a<em> fractional expression. </em> Moreover, the quotient of two <em>polynomials</em> such as:
is called a rational expression. So according to this definition rational expressions does not contain logarithmic functions. In fact, a rational expression is an expression that is the ratio of two polynomials like this:
Answer:
x = -2 or -9
Step-by-step explanation:
You want the values of x such that the line defined by the two points (2x+3, x+2) and (0, 2) is perpendicular to the line defined by the two points (x+2, -3-3x) and (8, -1).
<h3>Slope</h3>The slope of a line is given by the slope formula:
m = (y2 -y1)/(x2 -x1)
Using the formula, the slopes of the two lines are ...
m1 = (2 -(x+2))/(0 -(2x+3)) = (-x)/(-2x-3) = x/(2x +3)
and
m2 = (-1 -(-3-3x))/(8 -(x+2)) = (2+3x)/(6 -x)
<h3>Perpendicular lines</h3>The slopes of perpendicular lines have product of -1:
The values of x that satisfy this equation are x = -2 and x = -9. The attached graphs show the lines for each of these cases.
