Which of the following is the quotient of the rational expressions shown below?

1 answer:

soldier1979 [14.2K]3 years ago

7 0

We have two rational expressions. One in numerator and one in denominator.
Dividing by a fraction is equivalent to multiplying by its reciprocal. The rational expression in the denominator can be multiplied by taking its reciprocal to simplify the overall expression as shown below.

$\frac{ \frac{4x+1}{6x} }{ \frac{x}{3x-1} } \\ \\ 
= \frac{4x+1}{6x} * \frac{3x-1}{x} \\ \\ 
= \frac{(4x+1)(3x-1)}{6 x^{2} }$

There are no common factors, so the expression can be simplified any further.

You might be interested in

Circle X with a radius of 6 units and circle Y with a radius of 2 units are shown. Which steps would prove the circles similar?

SSSSS [86.1K]

Answer:

See bolded below.

Step-by-step explanation:

Take a look at the attachment below. It represents circle x and y, with respect to each of their radii. In each of the options we are given, we would have to translate and dilate the circles, by a fixed scale factor -

Now the first thing one would do is translate the circles so that they share a common center point, or in other words the center of one circle rests on the edge of the other circle. That way when dilating circle y, it may fit into circle x as it expands.

The second point is how much this smaller circle ( circle y ) has to expand. The radius of circle y being 2, has to increase by 3 times the value to equal the radius of circle x, and hence has to dilate by a scale factor of 3 as to match circle x,

<u><em>Solution = " Translate the circles so the center of one circle rests on the edge of the other circle, and dilate circle Y by a scale factor of 3 " / Option D</em></u>