Mathematics: The solution set of [tex] rac{x ^{2} }{x + 1} - 1 = rac{1}{x + 1} [/tex]isa) {-1, 2}b) {2}c) {0, 1}d) {1, -2}

4:14 into 2:7 2:7 is correct...

The solution set of [tex] \frac{x ^{2} }{x + 1}

Ответ:

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30.12.2021

Mathematics

B) {2}

Step-by-step explanation:

Subtracting the right side, we get ...

$\dfrac{x^2}{x+1}-1-\dfrac{1}{x+1}=0\\\\\dfrac{x^2-x-1-1}{x+1}=0\\\\\dfrac{(x-2)(x+1)}{x+1}=0\\\\x-2=0 \qquad\text{cancel like terms}\\\\x=2$

The quadratic has solutions x={-1, 2}, but x=-1 makes the original equation undefined. It is extraneous. The only valid solution is x = 2.

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Comment on this solution method

Often, subtracting one side of a rational equation so you get an equation of the form ( )/( ) = 0 will let you cancel common factors from numerator and denominator. This can help avoid any extraneous solutions. (You may still get an extraneous solution if a denominator factor appears at a higher power in the numerator. x³/x² = 0 reduces to x=0, but that is still extraneous.)

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The solution set of
$\frac{x ^{2} }{x + 1} - 1 = \frac{1}{x + 1}$
is
a) {-1, 2}
b) {2}
c) {0, 1}
d) {1, -2}

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The solution set of isa) {-1, 2}b) {2}c) {0, 1}d) {1, -2}

Ответ:

Ответ:

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The solution set of
$\frac{x ^{2} }{x + 1} - 1 = \frac{1}{x + 1}$
is
a) {-1, 2}
b) {2}
c) {0, 1}
d) {1, -2}