I was wondering if I solved these problems right?
Simplify the following:
3xy^2 4xz
______ + ______ = 7xyz
2y 3x _____
5
2(x-1) 3(x^2-4)
______ * ________ = 6(x-2)
4(x+2) 5x-5 ______
20
x^2-x-6 3(x^2-4)
________ / __________ = (x-3) (x+5)
7x+7 x^2+6x+5 ______________
21(x-2)
Wow, did you look how your typing showed up ??
I will take a "guess" what the last one is ....
(x^2 - x - 6)/(7x+7) ÷ 3(x^2-4)/(x^2+6x+5) = (x-3)(x+5)/(21(x-2))
(x-3)(x+2)/(7(x+1)) (x+1)(x+5)/(3(x+2)(x-2)) = (x-3)(x+5)/(21(x-2))
(x-3)(x+5)/(21(x-2) = (x-3)(x+5)/(21(x-2))
everything cancels for
1 = 1
so the equation is an identity and true for all values of x, except x ≠ -1, ± 2,
retype the others using brackets.
1)
(3xy^2)/(2y) + (4xz)/(3x)
2)
(2(x-1))/(4(x+2)) *(3(x^2-4))/(5x-5)
To check if you have solved the problems correctly, let's simplify the expressions step by step.
Problem 1:
Here's the expression:
(3xy^2/2y) + (4xz/3x) = 7xyz/5
To simplify the expression, you can follow these steps:
Step 1: Simplify each fraction individually:
The first fraction becomes (3x) because y^2/y simplifies to y.
The second fraction becomes (4z) because x cancels out.
Step 2: Combine the simplified fractions:
(3x + 4z) = 7xyz/5
So, you have simplified the expression correctly if you have reached this final result: (3x + 4z) = 7xyz/5.
Problem 2:
Here's the expression:
(2(x-1)/4(x+2)) * (3(x^2-4)/5x-5) = 6(x-2)/20
To simplify the expression, you can follow these steps:
Step 1: Simplify each fraction individually:
The first fraction can be further simplified. Inside the brackets, (x-1) cancels out with (x-2), and (x+2) cancels out with (x+2). The fraction becomes (2/4) = 1/2.
The second fraction can be further simplified by factoring the quadratic expression in the numerator: (x^2-4) = (x-2)(x+2). The fraction becomes (3(x-2)(x+2)/(5x-5)).
Step 2: Multiply the simplified fractions:
(1/2) * (3(x-2)(x+2)/(5x-5)) = 6(x-2)/20
So, you have simplified the expression correctly if you have reached this final result: 6(x-2)/20.
Problem 3:
Here's the expression:
(x^2-x-6)/(7x+7) ÷ (3(x^2-4)/(x^2+6x+5)) = (x-3)(x+5)/(21(x-2))
To simplify the expression, you can follow these steps:
Step 1: Change the division into multiplication by taking the reciprocal of the second fraction:
(x^2-x-6)/(7x+7) * [(x^2+6x+5)/(3(x^2-4))]
Step 2: Factorize the quadratic expressions:
(x^2-x-6)/(7(x+1)) * [(x+1)(x+5)/(3(x-2)(x+2))]
Step 3: Cancel out any common factors in the numerator and denominator:
[(x-3)(x+5)]/[(7(x+1))*(3(x-2)(x+2))]
Step 4: Simplify further if possible:
[(x-3)(x+5)]/[21(x+1)(x-2)(x+2)]
So, you have simplified the expression correctly if you have reached this final result: (x-3)(x+5)/[21(x+1)(x-2)(x+2)].
Now that you have the simplified expressions, you can compare your answers to see if they match.