Wagner Vega
09/07/2023 · High School
Calcular ' \( x \) ' en: \( \quad \frac{x+5}{x-4}=\frac{3 x+3}{x-1} \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
Solve the equation \( \frac{x+5}{x-4}=\frac{3x+3}{x-1} \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(\frac{x+5}{x-4}=\frac{3x+3}{x-1}\)
- step1: Find the domain:
\(\frac{x+5}{x-4}=\frac{3x+3}{x-1},x \in \left(-\infty,1\right)\cup \left(1,4\right)\cup \left(4,+\infty\right)\)
- step2: Cross multiply:
\(\left(x+5\right)\left(x-1\right)=\left(x-4\right)\left(3x+3\right)\)
- step3: Calculate:
\(x^{2}+4x-5=\left(x-4\right)\left(3x+3\right)\)
- step4: Calculate:
\(x^{2}+4x-5=3x^{2}-9x-12\)
- step5: Move the expression to the left side:
\(x^{2}+4x-5-\left(3x^{2}-9x-12\right)=0\)
- step6: Calculate:
\(-2x^{2}+13x+7=0\)
- step7: Factor the expression:
\(\left(-x+7\right)\left(2x+1\right)=0\)
- step8: Separate into possible cases:
\(\begin{align}&-x+7=0\\&2x+1=0\end{align}\)
- step9: Solve the equation:
\(\begin{align}&x=7\\&x=-\frac{1}{2}\end{align}\)
- step10: Check if the solution is in the defined range:
\(\begin{align}&x=7\\&x=-\frac{1}{2}\end{align},x \in \left(-\infty,1\right)\cup \left(1,4\right)\cup \left(4,+\infty\right)\)
- step11: Find the intersection:
\(\begin{align}&x=7\\&x=-\frac{1}{2}\end{align}\)
- step12: Rewrite:
\(x_{1}=-\frac{1}{2},x_{2}=7\)
La solución de la ecuación \( \frac{x+5}{x-4}=\frac{3x+3}{x-1} \) es \( x=-\frac{1}{2} \) o \( x=7 \).
Quick Answer
La solución de la ecuación es \( x=-\frac{1}{2} \) o \( x=7 \).
Answered by UpStudy AI and reviewed by a Professional Tutor
UpStudy ThothAI
Self-Developed and Ever-Improving
Thoth AI product is constantly being upgraded and optimized.
Covers All Major Subjects
Capable of handling homework in math, chemistry, biology, physics, and more.
Instant and Accurate
Provides immediate and precise solutions and guidance.
Try Now
Ask Tutors
Ask AI
10x
Fastest way to Get Answers & Solutions
By text
Enter your question here…
By image
Re-Upload
Submit