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ExtremeBDS [4]
3 years ago
13

Select the rational expression that is equivalent to the given expression below. 4/x-3

Mathematics
2 answers:
Aliun [14]3 years ago
7 0
To find the correct option we need to calculate each of the given options.
Option (1):
\frac{x+2}{x-3} /  \frac{4}{x+2} =  \frac{x+2}{x-3} *  \frac{x+2}{4} =  \frac{(x+2)^2}{4(x-3)}

Option (2):
\frac{x+2}{x-3} *  \frac{4}{x+2} =  \frac{4}{x-3}

Option (3):
\frac{x+2}{x-3} - \frac{4}{x+2} = \frac{(x+2)^2-4(x-3)}{(x-3)(x+2)}

option (4)
\frac{x+2}{x-3} + \frac{4}{x+2} = \frac{(x+2)^2+4(x-3)}{(x-3)(x+2)}


So, the correct answer is option (2)
Thepotemich [5.8K]3 years ago
7 0
The second one where there is multiplication.
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3 years ago
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Murrr4er [49]

Answer:

21

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4 0
3 years ago
How do you do these questions?
Doss [256]

Step-by-step explanation:

(a) Fₙ₋₁ > 0, so Fₙ₊₁ > Fₙ.  Each term is bigger than the one before it, so the function is increasing, meaning the series will diverge to infinity.

(b) Fₙ₊₁ / Fₙ = (Fₙ + Fₙ₋₁) / Fₙ

Divide.

Fₙ₊₁ / Fₙ = 1 + (Fₙ₋₁ / Fₙ)

Rewrite the second fraction using negative exponent.

Fₙ₊₁ / Fₙ = 1 + (Fₙ / Fₙ₋₁)⁻¹

Take the limit of both sides as n approaches infinity.

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Substitute with φ.

φ = 1 + φ⁻¹

Solve.

φ² = φ + 1

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φ = [ -(-1) ± √((-1)² − 4(1)(-1)) ] / 2(1)

φ = (1 ± √5) / 2

Since the ratio can't be negative:

φ = (1 + √5) / 2

4 0
2 years ago
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