Answer:
[tex]-2x^2+x+3=0[/tex]
[tex]-x^2+x+5=0[/tex]
Step-by-step explanation:
Algebraic Manipulation
Consists of applying basic rules of algebra to simplify or transform algebraic expressions into others.
We are required to rewrite two expressions as quadratics in standard form.
Question 1:
[tex]\displaystyle \frac{x}{2} = x^2 - \frac{3}{2}[/tex]
To get rid of the denominators, multiply by 2:
[tex]x=2x^2-3[/tex]
Move all the terms to the left side:
[tex]x-2x^2+3=0[/tex]
Order by degree:
[tex]\boxed{-2x^2+x+3=0}[/tex]
Question 2:
[tex]\displaystyle \frac{5}{x} + 1 = x[/tex]
Multiply by x (x must be different from 0):
[tex]5+x=x^2[/tex]
Move all the terms to the left side:
[tex]5+x-x^2=0[/tex]
Order by degree:
[tex]\boxed{-x^2+x+5=0}[/tex]
