Answer: [tex]\frac{-2\sqrt7}{4} \approx -1.764[/tex]
Step-by-step explanation:
It will be easier to work with variables in this problem, so let's take a= [tex]\sqrt{7}[/tex] and b=1.
We can then use cross multiplication to eventually cancel some terms and simplify.
[tex]\frac{a-b}{a+b} - \frac{a+b}{a-b}\\=\frac{(a-b)^2 - (a+b)^2}{(a+b)(a-b)}\\[/tex]
Here, we can use the difference of two squares property: [tex]x^2-y^2=(x+y)(x-y)[/tex]. Set x = a - b and y = a + b. The problem then turns into
[tex]\frac{(a-b)^2 - (a+b)^2}{(a+b)(a-b)}\\\\=\frac{(a-b+a+b)(a-b-a-b)}{(a+b)(a-b)}\\=\frac{(2a)(-2b)}{(a+b)(a-b)}\\=\frac{-4ab}{a^2-b^2}[/tex]
Here, it becomes much easier to just plug in the values for a and b. Doing so we get
[tex]\frac{-4ab}{a^2-b^2}\\=\frac{-4\sqrt7}{7-1}\\=\frac{-2\sqrt7}{3} \approx -1.764[/tex]
Hope this helps!
