Find R(x)=f(x)/g(x), where f(x) and g(x) are given
f(x)=2a^2+7a+5/5a+25
g(x)=a^2-2a-3/a^2+2a-15
Find R(x) with ÷
So far so good. Have you tried factoring each expression, to eliminate common factors? These all appear to factor easily.
Find R(x)= f(x)÷g(x)
F(x)=(2a^2+7a+5)/(5a+25)
G(x)= (a^2-2a-3)/(a^2+2a-15)
2(a+5)(a+1)/5(a+5)*(a+5)(a-3)/(a-3)(a+1)
=2(a+5)/5.
looks good to me.
To find R(x) = f(x) / g(x), we first need to simplify both f(x) and g(x):
Let's start with f(x):
f(x) = (2a^2 + 7a + 5) / (5a + 25)
To simplify f(x), we can factor the numerator and denominator if possible and cancel out any common factors. In this case, the numerator cannot be easily factored, so we'll move on to the denominator.
For g(x):
g(x) = (a^2 - 2a - 3) / (a^2 + 2a - 15)
Similarly, we can try factoring the numerator and denominator. The numerator can be factored as (a - 3)(a + 1), and the denominator can be factored as (a + 5)(a - 3). Notice that both have the factor (a - 3), so we can cancel it out.
g(x) = [(a - 3)(a + 1)] / [(a + 5)(a - 3)]
= (a + 1) / (a + 5)
Now that we have simplified f(x) and g(x), we can substitute them back into R(x):
R(x) = f(x) / g(x)
= [(2a^2 + 7a + 5) / (5a + 25)] / [(a + 1) / (a + 5)]
To divide fractions, we invert the divisor (the second fraction) and multiply:
R(x) = [(2a^2 + 7a + 5) / (5a + 25)] * [(a + 5) / (a + 1)]
Now, we can simplify R(x) further by multiplying the numerators and denominators:
R(x) = [(2a^2 + 7a + 5)(a + 5)] / [(5a + 25)(a + 1)]
Finally, we can expand and simplify the numerator and denominator:
R(x) = [2a^3 + 17a^2 + 42a + 25] / [5a^2 + 30a + 25]
Therefore, R(x) = (2a^3 + 17a^2 + 42a + 25) / (5a^2 + 30a + 25)