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Solve the rational equation $y^2=\frac{x^2-49}{x^2+49}$

Step-by-step Solution

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Solution

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Final answer to the problem

$y=\frac{\sqrt{x^2-49}}{\sqrt{x^2+49}},\:y=\frac{-\sqrt{x^2-49}}{\sqrt{x^2+49}}$
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Step-by-step Solution

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Removing the variable's exponent

$\sqrt{y^2}=\pm \sqrt{\frac{x^2-49}{x^2+49}}$

Learn how to solve integral calculus problems step by step online.

$\sqrt{y^2}=\pm \sqrt{\frac{x^2-49}{x^2+49}}$

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Learn how to solve integral calculus problems step by step online. Solve the rational equation y^2=(x^2-49)/(x^2+49). Removing the variable's exponent. Cancel exponents 2 and \frac{1}{2}. The power of a quotient is equal to the quotient of the power of the numerator and denominator: \displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}. As in the equation we have the sign \pm, this produces two identical equations that differ in the sign of the term \frac{\sqrt{x^2-49}}{\sqrt{x^2+49}}. We write and solve both equations, one taking the positive sign, and the other taking the negative sign.

Final answer to the problem

$y=\frac{\sqrt{x^2-49}}{\sqrt{x^2+49}},\:y=\frac{-\sqrt{x^2-49}}{\sqrt{x^2+49}}$

Explore different ways to solve this problem

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

Solve for ySolve for xFind the discriminantFind the derivativeSolve by implicit differentiationSolve for y'Find dy/dxDerivative

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Function Plot

Plotting: $y^2+\frac{-x^2+49}{x^2+49}$

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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

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Main Topic: Integral Calculus

Integration assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.

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