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# Solve the rational equation $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

## Step-by-step Solution

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###  Videos

$y=\sqrt{\frac{b^2\left(a^2-x^2\right)}{a^2}},\:y=-\sqrt{\frac{b^2\left(a^2-x^2\right)}{a^2}}$
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##  Step-by-step Solution 

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The least common multiple (LCM) of a sum of algebraic fractions consists of the product of the common factors with the greatest exponent, and the uncommon factors

$L.C.M.=a^2b^2$

Learn how to solve rational equations problems step by step online.

$L.C.M.=a^2b^2$

Learn how to solve rational equations problems step by step online. Solve the rational equation (x^2)/(a^2)+(y^2)/(b^2)=1. The least common multiple (LCM) of a sum of algebraic fractions consists of the product of the common factors with the greatest exponent, and the uncommon factors. Obtained the least common multiple (LCM), we place it as the denominator of each fraction, and in the numerator of each fraction we add the factors that we need to complete. Combine and simplify all terms in the same fraction with common denominator a^2b^2. Multiply both sides of the equation by a^2b^2.

$y=\sqrt{\frac{b^2\left(a^2-x^2\right)}{a^2}},\:y=-\sqrt{\frac{b^2\left(a^2-x^2\right)}{a^2}}$

##  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 xSolve for aSolve for ySolve for bFind the discriminantFind the derivativeSolve by implicit differentiationSolve for y'Find dy/dxDerivative

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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
Dx
|◻|
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

### Main Topic: Rational Equations

Rational or fractional equations are those equations that contain algebraic fractions, and where the variable or unknown appears in the denominator of at least one of those fractions.