Choose the appropriate simplified expression.
1. 8x^2-10x+3/6x^2+3x-3
2. (x^2-4/x^2-1)*(x+1/x^2+2x)
3. (7/5y+25)-(4/3y+15)
4. (x^2/x^2+2x+1)/(3x/x^2-1)
5. (2x+4/3x-3)*(12x-12/x+5)
6. (7/2xy^2)+(3/8x^2y)
7. (x^2-16/2x+8)/((x-4)^2/8x-32)
8. 5-(4x^2-5x+1/x^2-x)
9. 1/3x/5/6y
Use Quadratic Formula.
1. (x-3/4)(x-1/2) / (x-1/2)(x+1) =
(x-3/4) / (x+1).
2. (x+2)(x-2)/(x+1)(x-1) * (x+1)/x(x+2)= (x-2)/x(x+1).
3. (7y/5+25) - (4y/3+15) =
7y/5 + 25 - 4y/3 - 15 =
Common denominator = 15.
21y/15 + 25 - 20y/15 - 15 =
y/15 + 10.
1. To simplify the expression 8x^2-10x+3/6x^2+3x-3, we can simplify the numerator and denominator separately.
Numerator: 8x^2-10x+3
This expression cannot be factored further, so no further simplification is possible.
Denominator: 6x^2+3x-3
First, we can factor out a common factor of 3 from all three terms:
3(2x^2 + x - 1)
Now, we can attempt to factor the quadratic expression: 2x^2 + x - 1
To do this, we need to find two numbers whose product is -2 and whose sum is 1. The numbers are 2 and -1.
Therefore, we can factor the quadratic expression as:
2x^2 + x - 1 = (2x - 1)(x + 1)
Putting everything together, the simplified expression is:
(8x^2-10x+3)/(6x^2+3x-3) = (8x^2-10x+3)/(3(2x - 1)(x + 1))
To simplify the given expressions, follow these steps:
1. For the first expression, simplify the numerator and denominator separately first.
- The numerator: 8x^2 - 10x + 3
- The denominator: 6x^2 + 3x - 3
- Therefore, the simplified expression is: (8x^2 - 10x + 3) / (6x^2 + 3x - 3)
2. For the second expression, simplify the numerator and denominator separately first.
- The numerator: (x^2 - 4)
- The denominator: (x^2 - 1) * (x + 1)
- Therefore, the simplified expression is: (x^2 - 4) / ((x^2 - 1) * (x + 1))
3. For the third expression, subtract the fractions.
- The first fraction: 7 / (5y + 25)
- The second fraction: 4 / (3y + 15)
- Therefore, the simplified expression is: (7 / (5y + 25)) - (4 / (3y + 15))
4. For the fourth expression, divide the fractions.
- The numerator: x^2
- The denominator: (x^2 + 2x + 1) / (3x / (x^2 - 1))
- Therefore, the simplified expression is: x^2 / ((x^2 + 2x + 1) / (3x / (x^2 - 1)))
5. For the fifth expression, multiply the fractions.
- The first fraction: (2x + 4) / (3x - 3)
- The second fraction: (12x - 12) / (x + 5)
- Therefore, the simplified expression is: ((2x + 4) * (12x - 12)) / ((3x - 3) * (x + 5))
6. For the sixth expression, add the fractions.
- The first fraction: 7 / (2xy^2)
- The second fraction: 3 / (8x^2y)
- Therefore, the simplified expression is: (7 / (2xy^2)) + (3 / (8x^2y))
7. For the seventh expression, divide the fractions.
- The numerator: (x^2 - 16) / (2x + 8)
- The denominator: ((x - 4)^2) / (8x - 32)
- Therefore, the simplified expression is: ((x^2 - 16) / (2x + 8)) / (((x - 4)^2) / (8x - 32))
8. For the eighth expression, subtract the fractions.
- The first fraction: 5
- The second fraction: (4x^2 - 5x + 1) / (x^2 - x)
- Therefore, the simplified expression is: 5 - ((4x^2 - 5x + 1) / (x^2 - x))
9. For the ninth expression, multiply the fractions.
- The first fraction: (1 / (3x)) * (1 / (5 / 6y))
- Therefore, the simplified expression is: (1 / (3x)) * (1 / (5 / 6y))