Divide each expression and write the quotient in its simplest form. 5 p + 5 8 − 10 p ÷ 3 p + 3 2 ( 8 − 10 p ) \frac{5p+5}{8-10p}\div\frac{3p+3}{2(8-10p)}

This problem asks us to divide each expression and write the quotient in its simplest form. So we have five p plus five over eight minus 10 p divided by three p plus three over two times eight minus 10 p. So let's see how we can go about dealing with this. Well, remember the rule when it comes to dividing rational expressions. We can use keep, change, flip. So I'm gonna keep the five p plus five over eight minus 10 p. I'm going to change the division to multiplication, and then I'm going to flip the second fraction. So we'll have two times eight minus 10 p, and then all of that's going to be over three p plus three. Now what can I do from here? Well, this is a point where we want to focus on simplifying and factoring. So what I'm going to do is multiply straight across, and as I go through this step, I'm going to simplify what I can. Now one thing that I see is I have a five in common right about here. So I'm gonna pull that five out to the front, and then we're going to have p plus one, just dividing out five from each of these terms. Now it's going to be multiplied by two times eight minuteus 10 p. We've gone ahead and multiplied across, and we've reverse distributed this five. Now let's move to the denominator. Well, in the denominator I have eight minuteus 10 p, and that's being multiplied by three p plus three, which I can go ahead and pull out a three from each of these terms giving me times three times p plus one. Now after pulling everything out, notice what happens here, the p plus one in the numerator and denominator will cancel. The eight minus 10 p will cancel as well. So all we end up with in the numerator is five times two, which is 10, and all we end up in the denominator is three. So 10 over three is the simplified final answer to this expression when we divide, and that's how you can solve these types of problems.

8. Rational Expressions and Functions

Multiplying and Dividing Rational Expressions

Intermediate Algebra

8. Rational Expressions and Functions

Multiplying and Dividing Rational Expressions

Struggling with Intermediate Algebra?

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Multiple Choice

Divide each expression and write the quotient in its simplest form.
$\frac{5 p + 5}{8 - 10 p} \div \frac{3 p + 3}{2 (8 - 10 p)}$

$\frac{10}{3}$

$\frac{3}{10}$

$$\frac$53$

$$\frac$13$

Verified step by step guidance

Rewrite the division of fractions as multiplication by the reciprocal. The expression is: $\frac{5p+5}{8-10p} \div \frac{3p+3}{2(8-10p)}$. This becomes $\frac{5p+5}{8-10p} \times \frac{2(8-10p)}{3p+3}$.

Factor common terms in the numerators and denominators where possible. For example, factor \$5p+5$ as $5(p+1)$ and $3p+3$ as $3(p+1)$.

Substitute the factored forms back into the expression: $\frac{5(p+1)}{8-10p} \times \frac{2(8-10p)}{3(p+1)}$.

Cancel out common factors that appear in both numerator and denominator, such as $(p+1)$ and $(8-10p)$, to simplify the expression.

Multiply the remaining factors in the numerator and denominator to write the quotient in simplest form.

3:41m

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Struggling with Intermediate Algebra?

Divide each expression and write the quotient in its simplest form.5p+58−10p÷3p+32(8−10p)\(\frac{5p+5}{8-10p}\[\div\]\frac{3p+3}{2(8-10p)}\)

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Divide each expression and write the quotient in its simplest form.
$\frac{5 p + 5}{8 - 10 p} \div \frac{3 p + 3}{2 (8 - 10 p)}$