Question

Simplify the result if possible. 2x²+3x /(x-5)-(2x+55)/(x-5)

Answer 1

The result is:

`\[ (2x^2 + 3x)/(x - 5) - (2x + 55)/(x - 5) = (2x^2 + 3x - (2x + 55))/(x - 5) = (2x^2 + 3x - 2x - 55)/(x - 5) = (2x^2 + x - 55)/(x - 5) \]`

Step-by-step explanation:

The given expression is a complex fraction with two terms in the numerator, each having the common denominator \( (x - 5) \). To simplify, we combine the two terms in the numerator by subtracting the second term from the first. This involves distributing the subtraction through the parentheses in the numerator. This results in
`\( (2x^2 + 3x) - (2x + 55) \),`which can be further simplified by combining like terms.

Next, we simplify the numerator by combining like terms. In this case, we combine the
`\(2x\) terms and simplify \(3x - 2x\) to \(x\)`. The simplified numerator becomes
`\(2x^2 + x - 55\). The denominator remains \( (x - 5) \)`since it is common to both terms in the original expression.

Therefore, the simplified expression is
`\( (2x^2 + x - 55)/(x - 5) \).` This expression cannot be further simplified as the numerator does not factor further, and the denominator \( (x - 5) \) does not have common factors with the numerator. The final answer represents the simplified form of the given complex fraction.