How do you subtract #\frac { 3a + 5} { a - 4} - \frac { 6a + 7} { a - 4}#?

Question

Hazel Anglin · Accepted Answer

See the entire solution process below:

Because both fractions are over a common denominator we can subtract the numerators over the common denominator: #((3a + 5) - (6a + 7))/(a - 4)# Now, we can remove the terms from the parenthesis being careful to manage the signs of the individual terms correctly: #(3a + 5 - 6a - 7)/(a - 4)# Next, we can group the like terms in the numerator: #(3a - 6a + 5 - 7)/(a - 4)# Then, combine the like terms in the numerator: #((3 - 6)a + (5 - 7))/(a - 4)# #(-3a - 2)/(a - 4)# Or #-(3a + 2)/(a - 4)#

Genesis Allen · Answer

undefined To subtract the given expressions, $\frac{3a + 5}{a - 4} - \frac{6a + 7}{a - 4}$, you need to first ensure that the denominators are the same. In this case, both fractions have the same denominator $a - 4$, so you can directly subtract the numerators while keeping the denominator unchanged.

So, the result would be:

$$\frac{(3a + 5) - (6a + 7)}{a - 4}$$

Now, you can simplify the numerator:

$$(3a + 5) - (6a + 7)$$
$$= 3a + 5 - 6a - 7$$
$$= (3a - 6a) + (5 - 7)$$
$$= -3a - 2$$

Therefore, the expression simplifies to:

$$\frac{-3a - 2}{a - 4}$$