Solve m ( झ ) ( ज ) (4x ^ 2 + 25y ^ 2)/(4x ^ 2 - 25y ^ 2) - (2x - 5y)/(2x + 5y) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

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Question

$$\frac { 4 x ^ { 2 } + 25 y ^ { 2 } } { 4 x ^ { 2 } - 25 y ^ { 2 } } - \frac { 2 x - 5 y } { 2 x + 5 y }$$

Evaluate

$\frac{20xy}{4x^{2}-25y^{2}}$

Short Solution Steps

Factor $4x^{2}-25y^{2}$.

$$\frac{4x^{2}+25y^{2}}{\left(2x-5y\right)\left(2x+5y\right)}-\frac{2x-5y}{2x+5y}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $\left(2x-5y\right)\left(2x+5y\right)$ and $2x+5y$ is $\left(2x-5y\right)\left(2x+5y\right)$. Multiply $\frac{2x-5y}{2x+5y}$ times $\frac{2x-5y}{2x-5y}$.

$$\frac{4x^{2}+25y^{2}}{\left(2x-5y\right)\left(2x+5y\right)}-\frac{\left(2x-5y\right)\left(2x-5y\right)}{\left(2x-5y\right)\left(2x+5y\right)}$$

Since $\frac{4x^{2}+25y^{2}}{\left(2x-5y\right)\left(2x+5y\right)}$ and $\frac{\left(2x-5y\right)\left(2x-5y\right)}{\left(2x-5y\right)\left(2x+5y\right)}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{4x^{2}+25y^{2}-\left(2x-5y\right)\left(2x-5y\right)}{\left(2x-5y\right)\left(2x+5y\right)}$$

Do the multiplications in $4x^{2}+25y^{2}-\left(2x-5y\right)\left(2x-5y\right)$.

$$\frac{4x^{2}+25y^{2}-4x^{2}+10xy+10xy-25y^{2}}{\left(2x-5y\right)\left(2x+5y\right)}$$

Combine like terms in $4x^{2}+25y^{2}-4x^{2}+10xy+10xy-25y^{2}$.

$$\frac{20xy}{\left(2x-5y\right)\left(2x+5y\right)}$$

Expand $\left(2x-5y\right)\left(2x+5y\right)$.

$$\frac{20xy}{4x^{2}-25y^{2}}$$

Expand

$-\frac{20xy}{25y^{2}-4x^{2}}$

Short Solution Steps

Factor $4x^{2}-25y^{2}$.

$$\frac{4x^{2}+25y^{2}}{\left(2x-5y\right)\left(2x+5y\right)}-\frac{2x-5y}{2x+5y}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $\left(2x-5y\right)\left(2x+5y\right)$ and $2x+5y$ is $\left(2x-5y\right)\left(2x+5y\right)$. Multiply $\frac{2x-5y}{2x+5y}$ times $\frac{2x-5y}{2x-5y}$.

$$\frac{4x^{2}+25y^{2}}{\left(2x-5y\right)\left(2x+5y\right)}-\frac{\left(2x-5y\right)\left(2x-5y\right)}{\left(2x-5y\right)\left(2x+5y\right)}$$

Since $\frac{4x^{2}+25y^{2}}{\left(2x-5y\right)\left(2x+5y\right)}$ and $\frac{\left(2x-5y\right)\left(2x-5y\right)}{\left(2x-5y\right)\left(2x+5y\right)}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{4x^{2}+25y^{2}-\left(2x-5y\right)\left(2x-5y\right)}{\left(2x-5y\right)\left(2x+5y\right)}$$

Do the multiplications in $4x^{2}+25y^{2}-\left(2x-5y\right)\left(2x-5y\right)$.

$$\frac{4x^{2}+25y^{2}-4x^{2}+10xy+10xy-25y^{2}}{\left(2x-5y\right)\left(2x+5y\right)}$$

Combine like terms in $4x^{2}+25y^{2}-4x^{2}+10xy+10xy-25y^{2}$.

$$\frac{20xy}{\left(2x-5y\right)\left(2x+5y\right)}$$

Expand $\left(2x-5y\right)\left(2x+5y\right)$.

$$\frac{20xy}{4x^{2}-25y^{2}}$$