What is the simplified form of the quantity of x plus 9, all over the quantity of x plus 1 + the quantity of x minus 2, all over 5?

Question

prince1342 · Answer

attachment

mathstudent55 · Answer

This?

$\dfrac{x + 9}{x + 1} + \dfrac{x - 2}{5} $

prince1342 · Answer

Yep!

mathstudent55 · Answer

Since you are adding fractions, you need a common denominator.
What is the LCD of x + 1 and 5?

prince1342 · Answer

1, or x

mathstudent55 · Answer

No. It is the product of x + 1 and 5, or 5(x + 1).
Both fractions need to have that denominator, so each fraction has to be multiplied by a fraction that equals 1, so that each fraction will have the LCD as its denominator.

$\dfrac{x + 9}{x + 1} \times \dfrac{5}{5}+ \dfrac{x - 2}{5} \times \dfrac{x + 1}{x + 1}$

mathstudent55 · Answer

$\dfrac{5(x + 9)}{5(x + 1)} +\dfrac{(x- 2)(x + 1)}{5(x + 1)}$

Now add the fractions by adding the numerators and setting that sum over the LCD.

Then simplify the numerator, and try factoring to see if you can reduce the fraction.

prince1342 · Answer

how do i do that?

mathstudent55 · Answer

The numerators are added together and the sum is set over the common denominator.

$\dfrac{5(x + 9) + ( x - 2 )(x + 1) } {5(x + 1)} $

Now apply the distributive property to the left part of the numerator to distribute the 5, and use multiply the binomials on the right part of the numerator, for example, by using FOIL.