Rationalize the denominator in each expression. that is, rewrite the expression so that there is a rational expression in the denominator -9)/√(x-9))-9)/(√x+3))

explanations: we multiply with a rational surd

(x-9)*√(x+9)/(√(x-9)*√(x+9)

=(x-9)√(x+9)/

B.( x-9)/√x+3 =( x-9)*(√x-3)/(√x+3)*(√x-3)

= (x-9)*(√x-3)/x-9

=√x-3

no

step-by-step explanation:

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240