Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Multiply. Write your answer in simplest form.\newline2x−3x2×(4x+1)\frac{2x - 3}{x^2} \times (4x + 1)

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Multiply and divide rational expressionsright chevron icon

Full solution

Q. Multiply. Write your answer in simplest form.\newline2x−3x2×(4x+1)\frac{2x - 3}{x^2} \times (4x + 1)
  1. Identify Terms: Identify the terms to be multiplied. We have the fraction (2x−3)/x2(2x - 3)/x^2 and the binomial (4x+1)(4x + 1). To multiply these, we will apply the distributive property.
  2. Multiply Numerator: Multiply the numerator of the fraction by the binomial. This means we will distribute (2x−3)(2x - 3) across (4x+1)(4x + 1).\newlineCalculation: (2x−3)∗(4x+1)=2x∗4x+2x∗1−3∗4x−3∗1(2x - 3) * (4x + 1) = 2x * 4x + 2x * 1 - 3 * 4x - 3 * 1
  3. Perform Multiplication: Perform the multiplication from Step 22.\newlineCalculation: 2x×4x+2x×1−3×4x−3×1=8x2+2x−12x−32x \times 4x + 2x \times 1 - 3 \times 4x - 3 \times 1 = 8x^2 + 2x - 12x - 3
  4. Combine Like Terms: Combine like terms in the result from Step 33.\newlineCalculation: 8x2+2x−12x−3=8x2−10x−38x^2 + 2x - 12x - 3 = 8x^2 - 10x - 3
  5. Place Over Denominator: Place the result from Step 44 over the original denominator x2x^2.\newlineCalculation: (8x2−10x−3)/x2(8x^2 - 10x - 3) / x^2
  6. Simplify Expression: Simplify the expression by dividing each term in the numerator by x2x^2.\newlineCalculation: 8x2x2−10xx2−3x2=8−10x−3x2\frac{8x^2}{x^2} - \frac{10x}{x^2} - \frac{3}{x^2} = 8 - \frac{10}{x} - \frac{3}{x^2}
  7. Write Final Answer: Write the final answer in simplest form. The expression is already simplified as each term is divided by x2x^2.\newlineFinal Answer: 8−10x−3x28 - \frac{10}{x} - \frac{3}{x^2}

More problems from Multiply and divide rational expressions

Question
Evaluate the expression for t=−4.4 t = -4.4 .\newlineWrite your answer in simplest form.\newline` frac{t - 4}{t - 2} =` ____
Get tutor helpright-arrow

Posted 1 month ago

Question
Simplify. Write your answer using whole numbers and variables.\newlineg3g2−4g\frac{g}{3g^2 - 4g}
Get tutor helpright-arrow

Posted 2 months ago

Question
Simplify. Express your answer as a single fraction in simplest form. 32−5p33\frac{3}{2} - \frac{5p^3}{3} ______
Get tutor helpright-arrow

Posted 2 months ago

Question
Simplify. Express your answer as a single fraction in simplest form. \newline1+v5w31\frac{1 + \frac{v^5w}{3}}{1}\newline______
Get tutor helpright-arrow

Posted 2 months ago

Question
Solve for h h .\newline−5h−2=−4h−3 \frac{-5}{h - 2} = \frac{-4}{h - 3} \newlineThere may be 11 or 22 solutions.\newlineh= h = _____ or h= h = _____
Get tutor helpright-arrow

Posted 1 month ago

Question
What is the equation of the vertical asymptote of y=1x+9y = \frac{1}{x + 9} ? _____
Get tutor helpright-arrow

Posted 2 months ago

Question
What is the excluded value for y=1x−9−9y = \frac{1}{x - 9} - 9 ?\newline______
Get tutor helpright-arrow

Posted 2 months ago

Question
Simplify. Write your answer using whole numbers and variables.\newline9k+49k2+4k\frac{9k + 4}{9k^2 + 4k}\newline______
Get tutor helpright-arrow

Posted 2 months ago

Question
Divide. Write your answer in simplest form.\newlineg−110g3+25g2÷(g−1)\frac{g- 1}{10g^3 + 25g^2} \div (g- 1)\newline______
Get tutor helpright-arrow

Posted 2 months ago

Question
Simplify. Express your answer as a single fraction in simplest form. \newline5−3t31\frac{5 - \frac{3}{t^3}}{1}\newline______
Get tutor helpright-arrow

Posted 2 months ago

View all (113)