What is the difference x +5/ x +2 - x + 1/x ^2 + 2x?

The difference will be given by:
(x +5)/ (x +2) - (x + 1)/(x ^2 + 2x)
=(x +5)/ (x +2) - (x + 1)/[x (x + 2)]
the LCM is x(x+2)
thus the difference will be:
[x(x+5)-(x+1)]/(x (x + 2))
=[x^2+5x-x-1]/[x(x+2)]
=(x^2-4x-1)/[x(x+2)]

Answer:(x^2-4x-1)/[x(x+2)]

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kudzordzifrancis kudzordzifrancis · Answer 2 · 2018-12-08T18:48:47+01:00

ANSWER
The difference is,

[tex] \frac{ {x}^{2} + 4x - 1}{ {x}^{2} + 2x} [/tex]

EXPLANATION

To find the difference, we just have to simplify the expression.

The given expression is

[tex] \frac{x + 5}{x + 2} - \frac{(x + 1)}{ {x}^{2} + 2x} [/tex]

We factor the denominator of the second fraction to get,

[tex]=\frac{x + 5}{x + 2} - \frac{(x + 1)}{ x( x+ 2)} [/tex]

We can now see clearly that the LCM is

[tex]x(x + 2)[/tex]

We collect LCM to get,

[tex]=\frac{x(x + 5) - (x + 1)}{ x( x+ 2)} [/tex]
We now expand the bracket to obtain,

[tex]=\frac{ {x}^{2} + 5x - x - 1}{ {x}^{2} + 2x} [/tex]

This gives us,

[tex]=\frac{ {x}^{2} + 4x - 1}{ {x}^{2} + 2x} [/tex]