Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Simplify. Express your answer as a single fraction in simplest form. $\newline$ $\frac{d}{2} - \frac{4}{5}d$

View step-by-step help

View step-by-step help

Add and subtract rational expressions

Full solution

Q. Simplify. Express your answer as a single fraction in simplest form.

\newline

\frac{d}{2} - \frac{4}{5}d

Identify Common Denominator: Identify the common denominator for the fractions $\frac{d}{2}$ and $\frac{4}{5d}$ . Since the denominators are $2$ and $5d$ , the least common denominator (LCD) is $10d$ .
Rewrite Fractions: Rewrite each fraction with the common denominator of $10d$ . For the first fraction, multiply both the numerator and denominator of $\frac{d}{2}$ by $5d$ to get $\left(\frac{5d \times d}{2 \times 5d}\right) = \frac{5d^2}{10d}$ . For the second fraction, multiply both the numerator and denominator of $\frac{4}{5d}$ by $2$ to get $\left(\frac{4 \times 2}{5d \times 2}\right) = \frac{8}{10d}$ .
Combine Fractions: Combine the fractions over the common denominator. $\newline$ Now that both fractions have the same denominator, we can combine them as follows: $\newline$ $(\frac{5d^2}{10d}) - (\frac{8}{10d}) = \frac{5d^2 - 8}{10d}$ .
Simplify Expression: Simplify the expression if possible. $\newline$ In this case, the numerator $5d^2 - 8$ cannot be simplified further, and the denominator $10d$ is already in simplest form. Therefore, the expression is already in its simplest form.

More problems from Add and subtract rational expressions

Question

Evaluate the expression for

t = -4.4

\newline

Write your answer in simplest form.

\newline

` frac{t - 4}{t - 2} =` ____

Posted 7 months ago

Question

Simplify. Write your answer using whole numbers and variables.

\newline

\frac{g}{3g^2 - 4g}

Posted 5 months ago

Question

Simplify. Express your answer as a single fraction in simplest form.

\frac{3}{2} - \frac{5p^3}{3}

Posted 5 months ago

Question

Simplify. Express your answer as a single fraction in simplest form.

\newline

1 + \frac{v^5w}{3}

\newline

Posted 5 months ago

Question

h

\newline

\frac{-5}{h - 2} = \frac{-4}{h - 3}

\newline

1

2

\newline

h =

h =

Posted 7 months ago

Question

What is the equation of the vertical asymptote of

y = \frac{1}{x + 9}

Posted 9 months ago

Question

What is the excluded value for

y = \frac{1}{x - 9} - 9

\newline

Posted 9 months ago

Question

Simplify. Write your answer using whole numbers and variables.

\newline

\frac{9k + 4}{9k^2 + 4k}

\newline

Posted 9 months ago

Question

Divide. Write your answer in simplest form.

\newline

\frac{g- 1}{10g^3 + 25g^2} \div (g- 1)

\newline

Posted 9 months ago

Question

Simplify. Express your answer as a single fraction in simplest form.

\newline

\frac{5 - \frac{3}{t^3}}{1}

\newline

Posted 9 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant