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2 years ago

PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!! I CANNOT RETAKE THIS!! Simplify.

Mathematics

1 answer:

NNADVOKAT [17]2 years ago

8 0

Answer: $\frac{2x(5x + 1)}{4x - 1}$

<u>Step-by-step explanation:</u>

$\frac{4x^{3}-12x^{2}}{4x^{2}+7x - 2}$ ÷ $\frac{2x^{2}-6x}{5x^{2}+11x + 2}$

= $\frac{4x^{2}(x - 3)}{(4x - 1)(x + 2)}$ ÷ $\frac{2x(x - 3)}{(5x + 1)(x + 2)}$

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

= $\frac{2x(5x + 1)}{4x - 1}$

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Answer:

x = 2

Step-by-step explanation:

$\frac{1}{2} (x - 1) - \frac{1}{6} (x+1) = 0$

In an equation our aim is to find the value of what we are looking for as well as keeping the equation balanced. For example if we divided by 2 only from one side then the equation would change so it's an important rule to keep in mind when solving equations, that you need to keep both sides of the equation the same.

$\frac{1}{2} (x - 1) - \frac{1}{6} (x+1) = 0$

→ Expand the brackets

$\frac{1}{2} x- \frac{1}{2}-\frac{1}{6}x -\frac{1}{6} =0$

→ Multiply everything by 12 to make solving the equation easier

6x - 6 - 2x - 2 = 0

→ Simplify equation

4x - 8 = 0

→ Add 8 to both sides to isolate 4x

4x = 8

→ Divide by 4 on both sides to isolate x

x = 2

⇒ We can substitute x = 2 back into the equation to see if the solution is correct, if we get 0 on both sides then x = 2 is correct

$\frac{1}{2} (x - 1) - \frac{1}{6} (x+1) = 0$

⇒ Substitute in the values

$\frac{1}{2} (2-1)-\frac{1}{6} (2+1) = 0$

⇒ Simplify

$\frac{1}{2} (1)-\frac{1}{6} (3) = 0$

⇒ Simplify further

$\frac{1}{2} -\frac{1}{2} =0$

0 = 0

The solution x = 2 is correct

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