Question

What is the simplified form of the quantity of x plus 4, all over 5 + the quantity of x plus 5, all over 5 ?

1. the quantity of x squared plus 9x plus 20, all over 5
2. the quantity of 2x plus 9, all over 5
3. the quantity of x squared plus 9x plus 20, all over 25
4. the quantity of x plus 4, all over the quantity x plus 5

Answer 1

The simplified form of the expression is 2x + 9.

Step-by-step explanation:

To simplify the given expression, we first need to find a common denominator for the two fractions. In this case, the common denominator is 5.

To find the numerator, we multiply the numerator and denominator of each fraction by 5 to get:

((x+4)*5 + (x+5)*5) / 5

Expanding the expressions in the numerator gives:

(5x + 20 + 5x + 25) / 5

Combining like terms, we have:

(10x + 45) / 5

Dividing each term by 5, we get the simplified form:

2x + 9