Solve for x: (x/4)-(5/x)=(1/4)
how about multiplying each term by 4x ?
x^2 - 20 = x
x^2 - x - 20 = 0
solve for,
an easy one, it factors
Wouldn't it be x^2-20=4 since (1/4)•4x= (4x/4)? So that means it would be x^2-24=0, right? Where would I go from there?
...since (1/4)•4x= (4x/4)?
yup, and what is 4x/4 ?
isn't that x ?
so you know how to factor simple trinomials?
x^2 - x - 20 = 0
(x-5)(x+4) = 0
so x = 5 or x = -5
check:
if x = 5
5/4 - 5/5 = 5/4 - 1 = 1/4 , check!
if x = -4
-4/4 - 5/-4
= -1 + 5/4 = 1/4 , check!
my answers are correct
Ay, my bad. Thanks :) and you mean x=5 or x=-4 right?
right, x = 5 and x = -4,
my bad, lol
Haha its ok. Thanks for the help.
To solve for x in the equation (x/4) - (5/x) = (1/4), we need to clear the fraction and simplify the equation. Here's how we can do it step by step:
Step 1: Multiply every term in the equation by the least common denominator, which is 4x. This will eliminate the fractions.
4x * [(x/4) - (5/x)] = 4x * (1/4)
Step 2: Simplify both sides of the equation.
x^2 - 20 = x
Step 3: Move all terms to one side of the equation to set it to zero.
x^2 - x - 20 = 0
Step 4: Factor the quadratic equation.
(x - 5)(x + 4) = 0
Step 5: Set each factor equal to zero and solve for x.
x - 5 = 0 or x + 4 = 0
If we solve these equations separately, we find:
x = 5 or x = -4
Therefore, the solutions for x in the equation (x/4) - (5/x) = (1/4) are x = 5 and x = -4.