Hi can some one please help me simplify the expression and solve the equation.
v^2+6v+8/v^2+v-12 divided by v+2/2v-6
thank you.
v^2+6v+8 = (v+2)(v+4)
v^2+v-12 = (v-3)(v+4)
dividing that gives (v+2)/(v-3)
The final division gives
(v+2)/(v-3) * 2(v-3)/(v+2) = 2
There is no equation, just the expression
[(v+2)(v+4)][2(v-3)] /[(v+2)(v-3)(v+4)]
a lot of stuff is the same top and bottom
2 is left up top
1 is left down below :)
2
To simplify the expression and solve the equation, let's break it down step by step:
Step 1: Simplifying the expression
First, let's simplify the numerator of the expression v^2 + 6v + 8 / v^2 + v - 12.
The numerator can be factored as (v + 2)(v + 4). This can be done by finding two numbers whose sum is 6 (the coefficient of v) and whose product is 8. In this case, 2 and 4 satisfy these conditions.
Now, the expression becomes [(v + 2)(v + 4)] / v^2 + v - 12
Next, let's simplify the denominator, which is v + 2 / 2v - 6.
Similarly, the denominator can be factored as (v - 3)(2v - 6), which further simplifies to 2(v - 3).
Now, the expression becomes [(v + 2)(v + 4)] / [v^2 + v - 12] divided by [v + 2 / 2(v - 3)]
Step 2: Division of rational expressions
When dividing rational expressions, we invert the second expression and multiply:
[(v + 2)(v + 4)] / [v^2 + v - 12] * [2(v - 3)] / [v + 2]
Step 3: Simplify further
Now, we can simplify the expression by canceling out common factors:
[(v + 2)(v + 4)] / [v^2 + v - 12] * [2(v - 3)] / [v + 2] = (v + 4) * 2(v - 3) / (v^2 + v - 12) * (v + 2)
Step 4: Expand and simplify
To simplify further, let's expand and cancel out common factors:
2(v + 4)(v - 3) / [(v + 4)(v - 3)] * (v + 2) / (v^2 + v - 12)
The (v + 4) and (v - 3) terms cancel out:
2(v - 3) * (v + 2) / (v^2 + v - 12)
Finally, we have:
2(v - 3)(v + 2) / (v^2 + v - 12)
This is the simplified expression.
Please note that I have simplified the given expression based on assumptions about the intended grouping of terms. If there are any parentheses missing, make sure to include them correctly.