Final answer:
The original expression simplifies to (-3x³ + 7x) / (5x+8). To combine fractions, a common denominator must be foundwe cannot directly combine the fractions since the denominators are different.
Step-by-step explanation:
To simplify the expression (2x³+3x)/(5x+8)-(5x³-4x)/(5x+8), since the denominators are the same, we can combine the numerators. This gives us:((2x³+3x) - (5x³-4x)) / (5x+8)Expanding further, we get:2x³+3x - 5x³+4x, which simplifies to:(-3x³ + 7x) / (5x+8)For the expression (2)/(3)+(x+1)/(7x), we cannot directly combine the fractions since the denominators are different.To simplify the expression (2x³+3x)/(5x+8)-(5x³-4x)/(5x+8), since the denominators are the same, we can combine the numerators. This gives us:((2x³+3x) - (5x³-4x)) / (5x+8)Expanding further, we get:2x³+3x - 5x³+4x, which simplifies to:(-3x³ + 7x) / (5x+8)For the expression (2)/(3)+(x+1)/(7x), we cannot directly combine the fractions since the denominators are different.
First, we would have to find a common denominator and then sum the numerators accordingly.To simplify the expression (2x³+3x)/(5x+8) - (5x³-4x)/(5x+8), we can first find a common denominator, which in this case is (5x+8). When we combine the fractions, the denominators will cancel out:(2x³+3x)/(5x+8) - (5x³-4x)/(5x+8) = ((2x³+3x) - (5x³-4x))/(5x+8)Expanding the expression, we get:(2x³+3x - 5x³+4x)/(5x+8) = (-3x³+7x)/(5x+8).