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Solve the rational equation $\frac{5}{x-7}=\frac{2}{x-2}$

Step-by-step Solution

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Solution

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Final answer to the problem

$x=\frac{4}{-3}$
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Step-by-step Solution

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  • Solve for x
  • Find the derivative using the definition
  • Solve by quadratic formula (general formula)
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  • Find the derivative
  • Factor
  • Factor by completing the square
  • Find the roots
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Inverting the equation

Learn how to solve equations problems step by step online.

$\frac{x-7}{5}=\frac{x-2}{2}$

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Unlock the first 3 steps of this solution

Learn how to solve equations problems step by step online. Solve the rational equation 5/(x-7)=2/(x-2). Inverting the equation. Apply fraction cross-multiplication. Solve the product 2\left(x-7\right). Solve the product 5\left(x-2\right).

Final answer to the problem

$x=\frac{4}{-3}$

Exact Numeric Answer

$x=-1.3333333$

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Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

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Function Plot

Plotting: $\frac{5}{x-7}+\frac{-2}{x-2}$

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5
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7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

How to improve your answer:

Similar Problems Solved

$\frac{2}{x+1}=\frac{3}{x-1}$

$\frac{4}{x+2}=\frac{6}{x-2}$

$\frac{3}{x+1}-\frac{1}{2}=\frac{1}{3x+3}$

$\frac{2x+4}{5x}=\frac{2}{x}$

$\frac{5}{x-7}=\frac{2}{x-2}$

$\frac{2x+3}{3x}=\frac{x}{2x-3}$

$\frac{x+1}{x-2}=\frac{x-3}{x}$

Main Topic: Equations

In mathematics, an equation is a statement of an equality containing one or more variables. Solving the equation consists of determining which values of the variables make the equality true. In this situation, variables are also known as unknowns and the values which satisfy the equality are known as solutions.

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