Question

Find the sum

X-2
X+3
+
2x+ 1
2x²+2
x
+
1
2x+1
x2 +1

Answer 1

`</p><p> \huge\red{ \bold{\frac{2x + 1}{ {x}^(2) + 1} }}`

Explanation:

`\frac{x - 2}{ {x}^(2) + 1} + \frac{x + 3}{ {x}^(2) + 1} \\ \\ = \frac{x - 2 + x + 3}{ {x}^(2) + 1} \\ \\ = \frac{2x + 1}{ {x}^(2) + 1} \\ \\ \red{ \bold{\therefore \: \frac{x - 2}{ {x}^(2) + 1} + \frac{x + 3}{ {x}^(2) + 1}}} \blue{ \bold{ = }} \purple{ \bold{\frac{2x + 1}{ {x}^(2) + 1} }} \\`

Answer 2

I'm terrible at explaining so here's a screenshot

- Ripper

Explanation: