Express as a single fraction in its simplest form:
(x+7)/4x- (3x+2)/2x
To express as a single fraction, we need to find a common denominator.
The common denominator for 4x and 2x is 4x.
Therefore, we can rewrite the expression as:
[(x+7)(2x) - (3x+2)(4x)] / (4x * 2x)
Expanding the parentheses, we have:
(2x^2 + 14x - 12x^2 - 8x) / (8x^2)
Combining like terms, we get:
(-10x^2 + 6x) / (8x^2)
This fraction is already in its simplest form.
To simplify the given expression, we need to find a common denominator so that we can combine the fractions. The denominators in this case are 4x and 2x. We can find the least common multiple (LCM) of these two terms, which is 4x.
To make both fractions have the same denominator, we need to multiply both the numerator and denominator of the first fraction by 2, and the numerator and denominator of the second fraction by 4.
((x+7)/4x) - ((3x+2)/2x)
= ((x+7)(2)/(4x)(2)) - ((3x+2)(4)/(2x)(4))
= (2x+14)/(8x^2) - (12x+8)/(8x^2)
Now, we can combine the fractions by subtracting their numerators and keeping the common denominator.
= (2x+14 - (12x+8))/(8x^2)
= (2x+14 - 12x - 8)/(8x^2)
= (-10x + 6)/(8x^2)
The resulting expression in simplest form is (-10x + 6)/(8x^2).