Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve for all values of x. (x+2)/(x+6)=(1)/(x) Answer: x=

Solve for all values of x x .\newlinex+2x+6=1x \frac{x+2}{x+6}=\frac{1}{x} \newlineAnswer: x= x=

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Simplify variable expressions using propertiesright chevron icon

Full solution

Q. Solve for all values of x x .\newlinex+2x+6=1x \frac{x+2}{x+6}=\frac{1}{x} \newlineAnswer: x= x=
  1. Find Common Denominator: First, we need to find a common denominator to combine the fractions. The common denominator for (x+6)(x+6) and xx is x(x+6)x(x+6). We will multiply both sides of the equation by this common denominator to eliminate the fractions.\newlineCalculation: x+2x+6×x(x+6)=1x×x(x+6)\frac{x+2}{x+6} \times x(x+6) = \frac{1}{x} \times x(x+6)
  2. Multiply and Simplify: After multiplying both sides by the common denominator, we can simplify the equation.\newlineCalculation: (x+2)×x=1×(x+6)(x+2) \times x = 1 \times (x+6)
  3. Distribute and Simplify: Now, we distribute the xx on the left side and simplify the right side.\newlineCalculation: x2+2x=x+6x^2 + 2x = x + 6
  4. Bring Terms Together: Next, we bring all terms to one side to set the equation to zero and solve for xx.\newlineCalculation: x2+2x−x−6=0x^2 + 2x - x - 6 = 0
  5. Factor the Equation: Simplify the equation by combining like terms.\newlineCalculation: x2+x−6=0x^2 + x - 6 = 0
  6. Set Factors to Zero: Now, we need to factor the quadratic equation.\newlineCalculation: (x+3)(x−2)=0(x + 3)(x - 2) = 0
  7. Solve for x: To find the values of x, we set each factor equal to zero and solve for x.\newlineCalculation: x+3=0x + 3 = 0 or x−2=0x - 2 = 0
  8. Check Valid Solutions: Solving each equation gives us the values of xx.\newlineCalculation: x=−3x = -3 or x=2x = 2\newlineHowever, we must check these solutions in the original equation to ensure they do not make the denominator zero.
  9. Check Valid Solutions: Solving each equation gives us the values of xx.\newlineCalculation: x=−3x = -3 or x=2x = 2\newlineHowever, we must check these solutions in the original equation to ensure they do not make the denominator zero.Checking x=−3x = -3 in the original equation's denominators:\newline(x+6)(x+6) becomes (−3+6)(-3+6) which is 33, not zero.\newlinexx becomes −3-3, which is not zero.\newlineSo, x=−3x = -3 is a valid solution.
  10. Check Valid Solutions: Solving each equation gives us the values of xx.\newlineCalculation: x=−3x = -3 or x=2x = 2\newlineHowever, we must check these solutions in the original equation to ensure they do not make the denominator zero.Checking x=−3x = -3 in the original equation's denominators:\newline(x+6)(x+6) becomes (−3+6)(-3+6) which is 33, not zero.\newlinexx becomes −3-3, which is not zero.\newlineSo, x=−3x = -3 is a valid solution.Checking x=2x = 2 in the original equation's denominators:\newline(x+6)(x+6) becomes x=−3x = -322 which is x=−3x = -333, not zero.\newlinexx becomes x=−3x = -355, which is not zero.\newlineSo, x=2x = 2 is also a valid solution.

More problems from Simplify variable expressions using properties

Question
Combine the like terms to create an equivalent expression:\newline2s+(−4s)=02s+(-4s)=\boxed{\phantom{0}}
Get tutor helpright-arrow

Posted 9 months ago

Question
Combine the like terms to create an equivalent expression:\newline−4p+(−6p)=□-4p+(-6p)=\square
Get tutor helpright-arrow

Posted 10 months ago

Question
Combine the like terms to create an equivalent expression:\newline4z−(−3z)=□4z-(-3z)=\square
Get tutor helpright-arrow

Posted 10 months ago

Question
Combine the like terms to create an equivalent expression:\newliner+(−5r)=0r+(-5r)=\boxed{\phantom{0}}
Get tutor helpright-arrow

Posted 9 months ago

Question
Combine the like terms to create an equivalent expression:\newline−4p+(−2)+2p+3=-4p+(-2)+2p+3=
Get tutor helpright-arrow

Posted 10 months ago

Question
Rewrite the expression in the form k⋅zn k \cdot z^{n} .\newlineWrite the exponent as an integer, fraction, or an exact decimal (not a mixed number).\newline3z4⋅3z34= 3 \sqrt[4]{z} \cdot 3 z^{\frac{3}{4}}=
Get tutor helpright-arrow

Posted 9 months ago

Question
Let y=3x y=3^{x} .\newlineFind d2ydx2 \frac{d^{2} y}{d x^{2}} \newlined2ydx2= \frac{d^{2} y}{d x^{2}}=
Get tutor helpright-arrow

Posted 8 months ago

Question
Let y=4x2+3x2x−7 y=\frac{4 x^{2}+3 x}{2 x-7} .\newlinedydx= \frac{d y}{d x}=
Get tutor helpright-arrow

Posted 8 months ago

Question
ddx(excos⁡(x))= \frac{d}{d x}\left(\frac{e^{x}}{\cos (x)}\right)=
Get tutor helpright-arrow

Posted 5 months ago

Question
Let f(x)=1x2 f(x)=\frac{1}{x^{2}} .\newlinef′(5)= f^{\prime}(5)=
Get tutor helpright-arrow

Posted 8 months ago

View all (237)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant