To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90] and the first few multiples of 15 are [15, 30, 45, 60, 75, 90]. The first few multiples they share are [45, 90] making 45 the smallest multiple 9 and 15 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{4 x 5}{9 x 5} \) + \( \frac{2 x 3}{15 x 3} \)

\( \frac{20}{45} \) + \( \frac{6}{45} \)

Now, because the fractions share a common denominator, you can add them:

\( \frac{20 + 6}{45} \) = \( \frac{26}{45} \) = \(\frac{26}{45}\)

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:

4x⁴ - 3x⁴
(4 - 3)x⁴
x⁴

A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.

To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

3 + (3 + 5) ÷ 5 x 4 - 5²
P: 3 + (8) ÷ 5 x 4 - 5²
E: 3 + 8 ÷ 5 x 4 - 25
MD: 3 + \( \frac{8}{5} \) x 4 - 25
MD: 3 + \( \frac{32}{5} \) - 25
AS: \( \frac{15}{5} \) + \( \frac{32}{5} \) - 25
AS: \( \frac{47}{5} \) - 25
AS: \( \frac{47 - 125}{5} \)
\( \frac{-78}{5} \)
-15\(\frac{3}{5}\)