Add. $$ \frac{3}{2 x}+\frac{2}{x-4} $$ Simplify your answer as much as possible.

Question

UpStudy AI · Accepted Answer

Calculate or simplify the expression $$ \frac{3}{2x}+\frac{2}{x-4} $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\frac{3}{2x}+\frac{2}{x-4}$$
- step1: Reduce fractions to a common denominator:
  $$\frac{3\left(x-4ight)}{2x\left(x-4ight)}+\frac{2	imes 2x}{\left(x-4ight)	imes 2x}$$
- step2: Reorder the terms:
  $$\frac{3\left(x-4ight)}{2x\left(x-4ight)}+\frac{2	imes 2x}{2\left(x-4ight)x}$$
- step3: Rewrite the expression:
  $$\frac{3\left(x-4ight)}{2x\left(x-4ight)}+\frac{2	imes 2x}{2x\left(x-4ight)}$$
- step4: Transform the expression:
  $$\frac{3\left(x-4ight)+2	imes 2x}{2x\left(x-4ight)}$$
- step5: Multiply the terms:
  $$\frac{3x-12+2	imes 2x}{2x\left(x-4ight)}$$
- step6: Multiply the terms:
  $$\frac{3x-12+4x}{2x\left(x-4ight)}$$
- step7: Add the terms:
  $$\frac{7x-12}{2x\left(x-4ight)}$$
- step8: Multiply the terms:
  $$\frac{7x-12}{2x^{2}-8x}$$
The sum of the given fractions is $$\frac{7x-12}{2x^{2}-8x}$$.
The simplified sum is $$ \frac{7x - 12}{2x^{2} - 8x} $$.

Add. \[ \frac{3}{2 x}+\frac{2}{x-4} \] Simplify your answer as much as possible.

Solución de inteligencia artificial de Upstudy

Responder

Solución

Mind Expander

preguntas relacionadas

Latest Algebra Questions