Subtract simplify if possible.
5-v/v-8 - 9v-7/8-v
I can't do this no matter how I try i cannot figure out what the lcd is. I don't see where either denominator can be factored. WHat am I doing wrong?
8-v is the opposite of v-8, so 8-v = -(v-8)
now you have a common denominator
(5-v)/(v-8) - (9v-7)/(8-v)
= (5-v)/(v-8) + (9v-7)/(v-8)
= [5-v + 9v-7]/(v-8)
= (8v -2)/(v-8)
Once again you have come to my rescue. Thank you Reiny.
To simplify the given expression, we need to find a common denominator for the two fractions and then perform the subtraction. Let's break it down step by step:
1. Identify the denominators: The denominators in the expression are (v - 8) and (8 - v).
2. Write the two fractions with a common denominator: Since (v - 8) and (8 - v) are the same expression with opposite sign, we can rewrite the second fraction as (-1)*(v - 8), which gives us (9v - 7)/(-1)(v - 8).
3. Combine the two fractions: Now we have (5 - v)/(v - 8) - (9v - 7)/(-1)(v - 8).
4. Find the least common denominator (LCD): To find the LCD, we need to consider the factors of (v - 8) and (-1)(v - 8). Since (-1)(v - 8) is equal to (8 - v), we can see that the common denominator is (v - 8) * (8 - v).
5. Rewrite the fractions with the common denominator: Multiply the numerator and denominator of the first fraction by (8 - v), and multiply the numerator and denominator of the second fraction by (v - 8). This gives us:
[(5 - v)(8 - v)] / [(v - 8)(8 - v)] - [(9v - 7)(v - 8)] / [(v - 8)(8 - v)].
6. Perform the subtraction: Now we have a common denominator, so we can subtract the two fractions. Combine the numerators and keep the denominator:
[(5 - v)(8 - v) - (9v - 7)(v - 8)] / [(v - 8)(8 - v)].
7. Simplify if possible: Expand the numerator using the distributive property and simplify the polynomial:
[(40 - 5v - 8v + v^2) - (9v^2 - 64v - 7v + 56)] / [(v - 8)(8 - v)].
Simplifying further: (40 - 5v - 8v + v^2 - 9v^2 + 64v + 7v - 56) / [(v - 8)(8 - v)].
8. Combine like terms in the numerator: -8v^2 + 51v - 16 / [(v - 8)(8 - v)].
After performing these steps, we are left with the expression (-8v^2 + 51v - 16) / [(v - 8)(8 - v)]. This is the simplified form of the given expression.