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Solve the rational equation $\frac{x}{2x+7}=\frac{x-5}{x-1}$

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Solution

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Final answer to the problem

$x=-5,\:x=7$
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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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1

Apply fraction cross-multiplication

Learn how to solve equations problems step by step online.

$x\left(x-1\right)=\left(2x+7\right)\left(x-5\right)$

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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 x/(2x+7)=(x-5)/(x-1). Apply fraction cross-multiplication. Multiplying polynomials x and x-1. Multiplying polynomials 2x+7 and x-5. Multiply the single term x by each term of the polynomial \left(2x+7\right).

Final answer to the problem

$x=-5,\:x=7$

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Function Plot

Plotting: $\frac{x}{2x+7}+\frac{-x+5}{x-1}$

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4
5
6
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

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

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

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

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

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

$\frac{x}{2}=\frac{8}{x}$

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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