Which expression is equivalent to the following complex fraction? -2/x + 5/y / 3/y - 2/x

Mathematics

1 answer:

Tju [1.3M]2 years ago

7 0

Answer: $\frac{5x-2y}{3x-2y}$

Step-by-step explanation:

$\frac{-\frac{2}{x}+\frac{5}{y}}{\frac{3}{y}-\frac{2}{x}}$
Multiplying the numerator and denominator by xy,

$=\frac{-2y+5x}{3x-2y}\\\\=\frac{5x-2y}{3x-2y}$

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The rate of return is 8.15%

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For the first question, you need to find the rate that makes the present value of a stream of ten constant annual payments of $15,000 equal to the $100,000 investment.

The formula that returns the present value of a constant payment is called the annuity formula and is:

$Present\text{ }value=payment\times \bigg[\dfrac{1}{r}-\dfrac{1}{r(1+r)^t}\bigg]$

In your problem you know:

Present value: $100,000
payment: $15,000
r: ?
t: 10

You cannot solve for r directly. You must guess a value and calculate the right side of the equation until to you find the rate that makes it equal to 100,000.

Try 5%:

$\$15,000\times \bigg[\dfrac{1}{0.05}-\dfrac{1}{0.05(1+0.05)^{10}}\bigg]=\$115,826$