Is there anyone who can show me the steps?

Question

1 = 20 / x ² - 8 / x . What are the steps needed to get the answers 2 and 10 and is one of the answers negative?

Answer 1

You asked twice. :-)

Multiply the second fraction by x²/x² to get a common denominator. 20/x² - 8x/x² = 1 or (20-8x)/x² = 1.

Multiply every term by x² and you get 20-8x = x².

So you need to solve x² +8x -20 = 0. You can factor this as (x+10)(x-2) = 0 so your solutions are x = -10 or x = 2.

Enjoy!

Answer 2

first you would multiply both sides of the equation by the greatest common denominator which is (x^2).
1(x^2)= 20/x^2(x^2) - 8/x(x^2)
the x^2 and the one in the 20/x^2 would cancel out and the x in 8/x goes into x^2 once. so you would get:
x^2=20-8x
bring all the numbers to one side of the equation by subtracting 20 and adding 8x.
x^2+8x-20=0
solve by factoring
(x+10)(x-2)=0
solve for x
x+10=0
subtract 10
x-2=0
add 2
x=-10 x=2 are the answers.

Answer 3

1 = 20 / (x^2) - 8 / x
The LCD of this equation is x^2. Multiply each term on both sides of the equation by x^2.

(x^2)(1) = (x^2)(20) / (x^2) - (x^2)(8) / x
x^2 = 20 - 8x

Rewrite the quadratic equation in standard form.

x^2 +8x - 20 = 0
(x + 10)(x - 2) = 0
x + 10 = 0 or x - 2 = 0
x = -10 or x = 2

Answer 4

x² = 20 - 8x
x² + 8x - 20 = 0
(x + 10).(x - 2) = 0
x = - 10, x = 2

Answer 5

1=(20-8x)/x²
x²=20-8x
x²+8x-20=0
(x+10)(x-2)=0
x=-10,2

hope this helped u.