How do I write this problem as a single fraction? Sorry my addition button doesn't work.
2x plus 7y 2x plus 5y
____________ - ____________ plus 2
8x 2x
To write the problem as a single fraction, we can combine the two fractions and simplify.
First, let's find the common denominator for the two fractions. The denominators in the problem are 8x and 2x. To find the least common multiple (LCM) of these two expressions, we can take the product of the denominators and divide by their greatest common divisor (GCD).
The GCD of 8x and 2x is 2x since both terms have a factor of 2x.
Now, let's find the LCM of 8x and 2x:
LCM = (8x * 2x) / (2x)
= 16x^2 / (2x)
= 8x
The least common denominator is 8x.
Next, let's convert the fractions to have the same denominator, 8x:
(2x + 7y)/(8x) - (2x + 5y)/(2x) + 2
To get the first term to have a denominator of 8x, we need to multiply the numerator and denominator by 1/4, since (2x)/(8x) = 1/4:
((2x * 1/4) + 7y)/(8x) - (2x + 5y)/(2x) + 2
Simplifying this, we have:
(1/4 * 2x + 7y)/(8x) - (2x + 5y)/(2x) + 2
= (1/2x + 7y)/(8x) - (2x + 5y)/(2x) + 2
Now, let's combine the fractions into a single fraction:
((1/2x + 7y) - (2x + 5y))/(8x) + 2
Expanding the numerator:
(1/2x + 7y - 2x - 5y)/(8x) + 2
Combining like terms in the numerator:
(-2x + 1/2x + 7y - 5y)/(8x) + 2
Simplifying the numerator:
(-3x - 4y)/(2x) + 2
Now, rewrite the problem as a single fraction:
(-3x - 4y)/(2x) + 2
And that's the expression written as a single fraction.