The expressions are simplified to 2x and [tex]\frac{2}{(x+ 1)(x - 1)}[/tex]
How to simply the expressions
1.
Given the expression;
[tex]\frac{8x^2 - 4x}{4x - 2}[/tex]
Let's factorize the numerator;
[tex]\frac{2x( 4x - 2)}{4x - 2}[/tex]
Factor the common terms, we have;
2x
2. [tex]\frac{1}{x-1} - \frac{2}{x} + \frac{1}{x + 1}[/tex]
Find the Lowest common multiple
[tex]\frac{x(x+ 1) - 2 (x+ 1)(x - 1) + x(x-1)}{x(x-1)(x+ 1)}[/tex]
expand the brackets
[tex]\frac{x^2 + x -2(x^2 -x + x -1) + x^2 -x}{x(x-1)(x+ 1)}[/tex]
[tex]\frac{x^2+x - 2x^2 -2 + 2x + 2 + x^2 - x}{x(x+1) (x -1)}[/tex]
collect like terms
[tex]\frac{2x}{x(x+ 1) (x-1)}[/tex]
Divide common terms
[tex]\frac{2}{(x+ 1)(x - 1)}[/tex]
Thus, the expressions are simplified to 2x and [tex]\frac{2}{(x+ 1)(x - 1)}[/tex]
Learn more about algebraic expressions here:
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