how do you simplify
5-x
_______
x^2-20 to = 4
I will assume you meant this, and you meant solve
(5-x)/(x^2 - 20) = 4
then ....
4x^2 - 80 = 5-x
4x^2 + x - 85 = 0
x = (-1 ± √1361)/8
= appr 4.486 or -4.736
that is a division signs '
yes, and that is how I took it.
notice / is used to indicate division
To simplify the expression (5-x)/(x^2-20), we need to find the common factors that can be cancelled out and simplify further if possible. Let's break it down step by step:
1. First, let's factor the denominator, x^2 - 20:
x^2 - 20 can be written as (x + √20)(x - √20).
2. Now we can rewrite the expression as:
(5 - x) / ((x + √20)(x - √20)) = 4
3. Next, let's rewrite 4 as a fraction:
4 can be written as 4/1.
4. The expression becomes:
(5 - x) / ((x + √20)(x - √20)) = 4/1
5. Now, we can cross-multiply:
(5 - x) * 1 = 4 * ((x + √20)(x - √20))
6. Simplify the right side of the equation:
4((x + √20)(x - √20)) = 4(x^2 - √20^2)
= 4(x^2 - 20)
7. Expand the left side of the equation:
5 - x = 4(x^2 - 20)
8. Distribute the 4 on the right side of the equation:
5 - x = 4x^2 - 80
9. Rearrange the equation to standard form:
4x^2 - x - 85 = 0
At this point, we have simplified the expression and transformed it into the equation 4x^2 - x - 85 = 0. Further simplification requires solving the quadratic equation.