Based on the analysis of the provided image, the task is to
solve and simplify a series of mathematical expressions and equations. The worksheet contains problems from basic arithmetic to algebra, including fractions, linear equations, and polynomial division.
Here is a breakdown of the solutions for the visible problems:
Left Column
1.
Problem: `3/4 + 1/2`
*
Solution: To add these fractions, find a common denominator (which is 4).
* `3/4 + 1/2 = 3/4 + 2/4 = 5/4`
*
Answer: `5/4`
2.
Problem: `2x - 3 = 7`
*
Solution: Isolate the variable `x`.
* Add 3 to both sides: `2x = 10`
* Divide both sides by 2: `x = 5`
*
Answer: `x = 5`
3.
Problem: `(x^2 - 9) / (x - 3)`
*
Solution: Factor the numerator, which is a difference of squares.
* `(x^2 - 9) = (x - 3)(x + 3)`
* So, `(x^2 - 9) / (x - 3) = (x - 3)(x + 3) / (x - 3)`
* Cancel the common factor `(x - 3)` (assuming `x ≠ 3`).
* The simplified expression is `x + 3`.
*
Answer: `x + 3`
4.
Problem: `(x^2 - 4x - 5) / (x + 1)`
*
Solution: Factor the numerator.
* `(x^2 - 4x - 5) = (x - 5)(x + 1)`
* So, `(x^2 - 4x - 5) / (x + 1) = (x - 5)(x + 1) / (x + 1)`
* Cancel the common factor `(x + 1)` (assuming `x ≠ -1`).
* The simplified expression is `x - 5`.
*
Answer: `x - 5`
Right Column
1.
Problem: `(3x^2 - 10x + 8) / (x - 2)`
*
Solution: Perform polynomial long division or factor the numerator.
* Factoring the numerator: `(3x^2 - 10x + 8) = (3x - 4)(x - 2)`
* So, `(3x^2 - 10x + 8) / (x - 2) = (3x - 4)(x - 2) / (x - 2)`
* Cancel the common factor `(x - 2)` (assuming `x ≠ 2`).
* The simplified expression is `3x - 4`.
*
Answer: `3x - 4`
2.
Problem: `(2x^2 + 5x - 3) / (x + 3)`
*
Solution: Perform polynomial long division or factor the numerator.
* Factoring the numerator: `(2x^2 + 5x - 3) = (2x - 1)(x + 3)`
* So, `(2x^2 + 5x - 3) / (x + 3) = (2x - 1)(x + 3) / (x + 3)`
* Cancel the common factor `(x + 3)` (assuming `x ≠ -3`).
* The simplified expression is `2x - 1`.
*
Answer: `2x - 1`
In summary, the worksheet requires the student to perform various mathematical operations, including adding fractions, solving linear equations, and simplifying rational expressions by factoring and canceling common terms. The handwritten answers provided in the image are correct for the problems that were clearly visible.
Parent Tip: Review the logic above to help your child master the concept of solving using the quadratic formula worksheet.
