Perform the following steps using the equations below and synbolic variables and
ID: 2268144 • Letter: P
Question
Perform the following steps using the equations below and synbolic variables and equations: (a) Use a MATLAB function to expand the first equation, and then use the another to take that answer and simplify it. Do not suppress your final answer for either operation. Comment on if the (b) Extract the numerator and the denominator of the second expression. Then factor the numerator (c) Take the separated denominator, and using another MATLAB function, substitute each z variable (d) Using the separated numerator (Not Factored) from part (b), the modified denominator from simplified version is equivalent to the expression you started with of the expression. Do not suppress the final factored result. with an z, and every z variable with a part (c), as well as the simplified expression found in part (a), solve for each of the variables. Do not suppress the values for the final answers.Explanation / Answer
close all;
clear all;
syms x y z;
%%%% (a) %%%%
f=expand((1+x)*(3+x)*(y-z)) % expanding the given form
g=simplify(f) % simplifying the expanded form
%%%% (b) %%%%
h= (x^2+2*x*y+y^2)/(4*x+5*(y^2)-4*(z^2)+4) % Given rational fucntion
[n,d]=numden(h) % extracting the numerator and denominator
n_fact_form=simplify(n) % factorizaton of numerator
%%%% (c) %%%%
dm=subs(d,[x z],[z x]) % substituting z,x in place of x,z
%%%% (d) %%%%
[solx,soly,solz]=solve([n, dm, g],[x y z]) % soving for x,y,z using numerator and changed denominator and simplified expression in part(a)
Answers:
>> equaexp
f =
3*y - 3*z + 4*x*y - 4*x*z + x^2*y - x^2*z
g =
(y - z)*(x^2 + 4*x + 3)
h =
(x^2 + 2*x*y + y^2)/(5*y^2 - 4*z^2 + 4*x + 4)
n =
x^2 + 2*x*y + y^2
d =
5*y^2 - 4*z^2 + 4*x + 4
n_fact_form =
(x + y)^2
dm =
- 4*x^2 + 5*y^2 + 4*z + 4
solx =
2
-1
-3
soly =
-2
1
3
solz =
-2
-5/4
-13/4
From Part (a) the simplified expression is equivalent to given expression.