Answer :

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!