Question

What is the difference? StartFraction x + 5 Over x + 2 EndFraction minus StartFraction x + 1 Over x squared + 2 x EndFraction StartFraction x squared + 4 x minus 1 Over x (x + 2) EndFraction StartFraction x squared + 4 x + 1 Over x (x + 2) EndFraction StartFraction 4 Over negative 1 (x squared + x minus 2) EndFraction StartFraction x squared + 6 x + 1 Over x (x + 2) EndFraction

Answer 1

Answer:

b

Step-by-step explanation:

Answer 2

The difference between the two given fractions is $\frac{x^2 + 4x - 1}{x^2 + 2x}$.

The given parameters:

$\frac{x + 5}{x + 2} - \frac{x+ 1}{x^2 + 2x}$

The difference between the two fractions is calculated as follows;

$\frac{x + 5}{x + 2} - \frac{x+ 1}{x^2 + 2x}\\\\= \frac{x + 5}{x + 2} - \frac{x+ 1}{x(x + 2)}$

The lowest common multiple (L.C.M) of the two denominators = x(x + 2)

$= \frac{x(x + 5) - (x + 1)}{x(x + 2)} \\\\= \frac{x^2 + 5x - x - 1}{x^2 + 2x} \\\\= \frac{x^2 + 4x - 1}{x^2 + 2x}$

Thus, the difference between the two given fractions is $\frac{x^2 + 4x - 1}{x^2 + 2x}$.

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