Questions: Perform the multiplication or division and simplify. (x^2+4x-5)/(x^2-25) * (x-5)/(x+4)

Perform the multiplication or division and simplify. (x^2+4x-5)/(x^2-25) * (x-5)/(x+4)
Transcript text: Perform the multiplication or division and simplify. \[ \frac{x^{2}+4 x-5}{x^{2}-25} \cdot \frac{x-5}{x+4} \]
failed

Solution

failed
failed

Solution Steps

To simplify the given expression, we need to factorize the polynomials in the numerators and denominators, cancel out common factors, and then perform the multiplication.

  1. Factorize \(x^2 + 4x - 5\) and \(x^2 - 25\).
  2. Simplify the expression by canceling out common factors.
  3. Multiply the remaining fractions.
Step 1: Factorize the Polynomials

We start by factorizing the polynomials in the numerators and denominators.

\[ x^2 + 4x - 5 = (x - 1)(x + 5) \] \[ x^2 - 25 = (x - 5)(x + 5) \]

Step 2: Substitute the Factored Forms

Substitute the factored forms into the original expression:

\[ \frac{(x - 1)(x + 5)}{(x - 5)(x + 5)} \cdot \frac{x - 5}{x + 4} \]

Step 3: Cancel Common Factors

Cancel the common factors \((x + 5)\) and \((x - 5)\) from the numerator and the denominator:

\[ \frac{(x - 1)}{(x + 4)} \]

Final Answer

The simplified expression is:

\[ \boxed{\frac{x - 1}{x + 4}} \]

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
6+42x+6=14
failedAnswered
During a well-child care visit, the mother of a 4 -year-old child reports her son is extremely active at home and cries easily if frustrated. This is consistent with which level of the classic temperament theory? slow-to-warm-up temperament flexible temperament difficult temperament complex temperament SUBMIT ANSWER
failedAnswered
Texarkana Electric Company burns coal to heat the water that drives its electricity-producing turbines. The table below shows the marginal benefit of annual electricity consumption and the private marginal cost of annual electricity production. Marginal Cost and Marginal Benefit Quantity (millions of megawatts) MBprivate MCprivate MC external MC social --------------- 0.5 145 85 20 105 1.0 130 90 20 110 1.5 115 95 20 115 2.0 100 100 20 120 2.5 85 105 20 125 3.0 60 110 20 130 Instructions: In parts a and b, enter your answers as a whole number. In part c, round your answer to one decimal place. a. What is "private quantity" of electricity Texarkana Electric Company will produce each year? million megawatts per year Now assume the production of electricity also produces sulfur dioxide (a precursor to acid rain). The external cost of the sulfur dioxide increases by 20 for each 0.5 million megawatts produced. b. Fill in the external marginal cost (MC external) and the social marginal cost (MC social) columns in the table above. c. What is the socially optimal amount of electricity for Texarkana to produce if all costs and benefits are considered? million megawatts per year
failedAnswered
(7x + 11)/8 = -3
failedAnswered
Standard deviation refers to the A. statistics used to organize, summarize, and describe sample data B. value within a given set of data in its original form C. average distance between variable scores and the mean in a set of data D. difference between the largest and smallest variable scores in a set of data Please select the best answer from the choices provided A B C D