When you simplify the numerator and the denominator, you find they both have denominators of xy. So, the ratio of those is the ratio of their numerators.

$\dfrac{\dfrac{2}{x}-\dfrac{4}{y}}{\dfrac{-5}{y}+\dfrac{3}{x}}=\dfrac{\left(\dfrac{2y-4x}{xy}\right)}{\left(\dfrac{-5x+3y}{xy}\right)}=\dfrac{2y-4x}{-5x+3y}\\\\=\boxed{\dfrac{2(y-2x)}{3y-5x}}$

8 0

2 years ago

Read 2 more answers

What two numbers add up to 45 and multiply and get 121

umka2103 [35]

Let the two numbers be x and y.

We have x+y=45
⇒ y= 45-x.

The two numbers multiply and get 121, so we have another equation:
x*y = 121 (1)

Plug y= 45-x in (1), we have:
x* (45-x)=121
⇒ 45x - x^2 = 121 (distributive property)
⇒ x^2 - 45x = -121 (multiply -1 on both sides)
⇒ x^2- 45x + 121= 0
⇒ x= 42.128 or x= 2.872

y= 45- 42.128= 2.872
or y= 45- 2.872= 42.128.

Because it does not matter what number, x or y, is larger, the two numbers are 2.872 and 42.128.

Hope this helps~

4 0

2 years ago