Flynn Bird
08/30/2023 · Middle School
- \( \frac{y}{x-y}=x^{2}+1 \rightarrow \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
Para resolver la ecuación \( \frac{y}{x-y} = x^{2} + 1 \), primero multiplicamos ambos lados por \( x - y \) para eliminar el denominador:
\[
y = (x^{2} + 1)(x - y)
\]
Ahora, distribuimos el lado derecho:
\[
y = (x^{2} + 1)x - (x^{2} + 1)y
\]
Esto se simplifica a:
\[
y + (x^{2} + 1)y = (x^{2} + 1)x
\]
Factorizamos \( y \) en el lado izquierdo:
\[
y(1 + (x^{2} + 1)) = (x^{2} + 1)x
\]
Simplificamos el término en paréntesis:
\[
y(1 + x^{2} + 1) = (x^{2} + 1)x
\]
\[
y(2 + x^{2}) = (x^{2} + 1)x
\]
Finalmente, despejamos \( y \):
\[
y = \frac{(x^{2} + 1)x}{2 + x^{2}}
\]
Así que la solución para \( y \) en términos de \( x \) es:
\[
y = \frac{(x^{2} + 1)x}{2 + x^{2}}
\]
Quick Answer
Para resolver la ecuación \( \frac{y}{x-y} = x^{2} + 1 \), multiplicamos ambos lados por \( x - y \), distribuimos y factorizamos, luego despejamos \( y \) para obtener \( y = \frac{(x^{2} + 1)x}{2 + x^{2}} \).
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