Multiplying StartFraction 3 Over StartRoot 17 EndRoot minus StartRoot 2 EndRoot EndFraction by which fraction will produce an equivalent fraction with a rational denominator? StartFraction StartRoot 17 EndRoot minus StartRoot 2 EndRoot Over StartRoot 17 EndRoot minus StartRoot 2 EndRoot EndFraction StartFraction StartRoot 17 EndRoot + StartRoot 2 EndRoot Over StartRoot 17 EndRoot + StartRoot 2 EndRoot EndFraction StartFraction StartRoot 2 EndRoot minus StartRoot 17 EndRoot Over StartRoot 2 EndRoot minus StartRoot 17 EndRoot EndFraction StartFraction StartRoot 15 EndRoot Over StartRoot 15 EndRoot EndFraction

step-by-step explanation:

12475909

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2

(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