Question

Simplifique a expressão combinando termos equivalentes.
A) 2x + 5x + 7 + y -3x + 4y + 2
B) 4 + 2x - 3z + 5y - x + 2y - z - 2

Use a propriedade distributiva para expandir os produtos. Simplifique a expressão resultante combinando termos semelhantes.
A) 3(2x - y) + 4(y - x) + x + y
B) 5(2x + y - 1) + 4(y - 3x + 2) + 1

Reduza as frações ao mesmo denominador para operar com as frações. Simplifique a fração resultante.
A) 2/y + 3/y
B) 1/y-1 + 3/y-2
C) 2 + 1/x
D) 1/x + 1/y - x
E) x+4/2 + 3x-1/5
F)x/3 + x/4

Answer 1

Resposta:

A)4x+5y+9

B)2+x+7y-4z

Answer 2

Resposta:

1. a) 4x+5y+9

b) x+7y+2-4z

2. a) 3x+2y

b) 9y+4-2x

3. a) $\frac{5}{y}$

b)$\frac{4y-5}{\left(y-1\right)\left(y-2\right)}$

c)$\frac{2x+1}{x}$

d)$\frac{y+x-x^2y}{xy}$

e)$4x+\frac{9}{5}$

f)$\frac{7x}{12}$

Explicação passo-a-passo:

$2x+5x+7+y-3x+4y+2=2x+5x-3x+y+4y+7+2=4x+y+4y+7+2=4x+5y+9\\\\4+2x-3z+5y-x+2y-z-2=2x-x-3z-z+5y+2y+4-2=x-3z-z+5y+2y+4-2=x-4z+5y+2y+4-2=x-4z+7y+4-2=x+7y+2-4z\\\\3\left(2x-y\right)+4\left(y-x\right)+x+y=6x-3y+4\left(y-x\right)+x+y=6x-3y+4y-4x+x+y=3x+2y\\\\5\left(2x+y-1\right)+4\left(y-3x+2\right)+1=10x+5y-5+4\left(y-3x+2\right)+1=10x+5y-5+4y-12x+8+1=9y+4-2x\\\\\frac{2}{y}+\frac{3}{y}=\frac{2+3}{y}=\frac{5}{y}$

$\frac{1}{y-1}+\frac{3}{y-2}=\frac{y-2}{\left(y-1\right)\left(y-2\right)}+\frac{3\left(y-1\right)}{\left(y-2\right)\left(y-1\right)}=\frac{y-2+3\left(y-1\right)}{\left(y-1\right)\left(y-2\right)}=\frac{4y-5}{\left(y-1\right)\left(y-2\right)}\\\\2+\frac{1}{x}=\frac{2x}{x}+\frac{1}{x}=\frac{2x+1}{x}\\\\\frac{1}{x}+\frac{1}{y}-x=\frac{1}{x}+\frac{1}{y}-\frac{x}{1}=\frac{y}{xy}+\frac{x}{xy}-\frac{x^2y}{xy}=\frac{y+x-x^2y}{xy}$

$x+\frac{4}{2}+3x-\frac{1}{5}=x+3x+\frac{4}{2}-\frac{1}{5}=4x+\frac{4}{2}-\frac{1}{5}=4x+2-\frac{1}{5}=\frac{2\cdot \:5}{5}-\frac{1}{5}=\frac{2\cdot \:5-1}{5}=4x+\frac{9}{5}\\\\\frac{x}{3}+\frac{x}{4}=\frac{x\cdot \:4}{12}+\frac{x\cdot \:3}{12}=\frac{x\cdot \:4+x\cdot \:3}{12}=\frac{7x}{12}$