Divide through everything by <em>b</em> :

Since <em>a/b</em> < <em>c/d</em>, it follows that

Multiply through everything on the right side by <em>b/d</em> to get

and so (<em>a</em> + <em>c</em>)/(<em>b</em> + <em>d</em>) < <em>c/d</em>.
For the other side, you can do something similar and divide through everything by <em>d</em> :

and <em>a/b</em> < <em>c/d</em> tells us that

Then

and so (<em>a</em> + <em>c</em>)/(<em>b</em> + <em>d</em>) > <em>a/b</em>.
Then together we get the desired inequality.
<h2>•5×7^2</h2>
<em>HOPE</em><em> </em><em>ITS</em><em> </em><em>HELPFUL</em><em> </em>^_^
<h2>
•RHONA</h2>
Answer:
a. addition property of Equality
I believe the center would be (-4,2) while the radius should be 3.