Hello need help please with Divide rational and simplify

1 answer:

5 0

Dividing fractions is the same as multiplying by its reciprocal so you can change the equation to this
$\frac{ - 14 + 7x}{4} \times \frac{4}{4 - 2x}$
And you can simplify by eliminating the fours and multiplying straight across
$\frac{ - 14 + 7x}{4 - 2x}$
You can pull out - 7 from the top and 2 from the bottom so you have this
$\frac{ - 7(2 - x)}{2(2 - x)}$
And then you can cancel out to (2-x) to get an answer of
$\frac{ - 7}{2}$

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The slope is 3.

Step-by-step explanation:

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$\frac{4}{ \frac{1}{4} - \frac{5}{2} }$

To begin, we can simplify the expression's denominator by finding a common denominator between the denominators of the fractions in the denominator. To make them compatible, we can convert $\frac{5}{2}$ into $\frac{10}{4}$ :

$\frac{4}{ \frac{1}{4} - \frac{5}{2}( \frac{2}{2}) } = \frac{4}{ \frac{1}{4} - \frac{10}{4} }$

Next, we can simplify:

$\frac{4}{ \frac{1}{4} - \frac{10}{4} } = \frac{4}{ -\frac{9}{4}}$

Finally, to cancel the denominator within the denominator, we can multiply the whole expression by $\frac{4}{4}$ , or 1:

$\frac{4}{ -\frac{9}{4}}* \frac{4}{4} = -\frac{16}{9}$

The expression simplifies to $-\frac{16}{9}$ , or $-1 \frac{7}{9}$ as a mixed number.