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2 years ago

Write as a single fraction in its simplest form.

Mathematics

1 answer:

yaroslaw [1]2 years ago

5 0

$\dfrac{4}{3x-5} + \dfrac{x+2}{x-1}\\\\\\=\dfrac{4(x-1) + (x+2)(3x-5)}{(3x-5)(x-1)}\\\\\\=\dfrac{4x-4 + 3x^2 -5x +6x -10}{(3x-5)(x-1)}\\\\\\=\dfrac{3x^2 +5x-14}{(3x-5)(x-1)}$

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What is the product? startfraction 4 k 2 over k squared minus 4 endfraction times startfraction k minus 2 over 2 k 1 endfraction

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The product of the expression $(\frac{4k+2}{k^2-4})* \frac{k-2}{2k+1}$ is the expression $\frac{2}{k+2}$

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more variables and numbers.

Given the expression:

$(\frac{4k+2}{k^2-4})* \frac{k-2}{2k+1} \\\\This\ can\ be\ simplified\ to:\\\\(\frac{2(2k+1)(k-2)}{(k+2)(k-2)(2k+1)}) \\\\=\frac{2}{k+2}$

The product of the expression $(\frac{4k+2}{k^2-4})* \frac{k-2}{2k+1}$ is the expression $\frac{2}{k+2}$

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2 years ago

Circles are described below by the coordinates of their centers, C, and one point on their circumference, A. Determine an equati

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Using the given center and point at the circumference, the equation of the circles are:

a) $(x - 5)^2 + (y - 2)^2 = 100$

b) $(x + 2)^2 + (y + 5)^2 = 169$

c) $(x - 5)^2 + (y + 1)^2 = 65$

<h3>What is the equation of a circle?</h3>

The equation of a circle of radius r and center $(x_0,y_0)$ is given by:

$(x - x_0)^2 + (y - y_0)^2 = r^2$

Item a:

Center C(5,2), hence $x_0 = 5, y_0 = 2$ .

The point at the circumference is A(11,10), hence:

$(x - 5)^2 + (y - 2)^2 = r^2$

$(11 - 5)^2 + (10 - 2)^2 = r^2$

$r^2 = 100$

Hence:

$(x - 5)^2 + (y - 2)^2 = 100$

Item b:

Center C(-2,-5), hence $x_0 = -2, y_0 = -5$ .

The point at the circumference is A(3,-17), hence:

$(x + 2)^2 + (y + 5)^2 = r^2$

$(3 + 2)^2 + (-17 - 5)^2 = r^2$

$r^2 = 169$

Hence:

$(x + 2)^2 + (y + 5)^2 = 169$

Item c:

Center C(5,-1), hence $x_0 = 5, y_0 = -1$ .

The point at the circumference is A(-2,-5), hence:

$(x - 5)^2 + (y + 1)^2 = r^2$

$(-2 - 5)^2 + (-5 + 1)^2 = r^2$

$r^2 = 65$

Hence:

$(x - 5)^2 + (y + 1)^2 = 65$

You can learn more about equation of a circle at brainly.com/question/24307696

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