Solve for x : 1 x+1 +3 5 x+1 =5 x+4 , x -1,-1 5 ,-4 - Vidyadip

Question

Solve for $x$ :
$\frac{1}{x+1}+\frac{3}{5 x+1}=\frac{5}{x+4}, x \neq-1,-\frac{1}{5},-4$

✓

Answer

$\begin{array}{l}\frac{1}{x+1}+\frac{3}{5 x+1}=\frac{5}{x+4}, x \neq-1,-\frac{1}{5},-4 \\ \Rightarrow \frac{5 x+1+3 x+3}{(x+1)(5 x+1)}=\frac{5}{x+4} \\ \Rightarrow(x+4)(8 x+4)=5(x+1)(5 x+1) \\ \Rightarrow(x+4)(8 x+4)=5(x+1)(5 x+1) \\ \Rightarrow 8 x^2+32 x+4 x+16=5\left(5 x^2+x+5 x+1\right)\end{array}$
$\begin{array}{l}\Rightarrow 8 x^2+36 x+16=25 x^2+30 x+5 \\ \Rightarrow 17 x^2-6 x-11=0 \\ \Rightarrow 17 x^2-17 x+11 x-11=0 \\ \Rightarrow 17 x(x-1)+11(x-1)=0 \\ \Rightarrow(17 x+11)(x-1)=0 \\ \Rightarrow 17 x+11=0 \text { or } x-1=0 \\ \Rightarrow x=-\frac{11}{17} \text { or } x=1\end{array}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "5 Marks Questions" from Quadratic Equations→Quadratic Equations — all question types→Maths STD 10 question papers→CBSE Board STD 10 question papers→CBSE Board question paper generator→

Similar questions

If $\text{x}=\cot\text{A}+\cos\text{A}$ and $\text{y}=\cot\text{A}-\cos\text{A},$ Prove that $\Big(\frac{\text{x}-\text{y}}{\text{x}+\text{y}}\Big)^2+\Big(\frac{\text{x}-\text{y}}{2}\Big)^2=1.$

The sum of $4^{\text {th }}$ and $8^{\text {th }}$ terms of an A.P. is 24 and the sum of the $6^{\text {th }}$ and $10^{\text {th }}$ terms is 34 . Find the first term and the common difference of the A.P.

If G be the centroid of a triangle ABC, prove that:
$AB^2 + BC^2 + CA^2 = 3(GA^2 + GB^2 + GC^2)$

If the price of a book is reduced by $₹\ 5,$ a person can buy $5$ more books for $₹\ 300$. Find the original list price of the book.

Solve the given pair of linear equation by the elimination method and the substitution method: 3x + 4y = 10 and 2x – 2y = 2

Draw a circle of radius 3cm. Draw a tangent to the circle making an angle of 30° with a line passing through the centre.

Write the expression $a_n - a_k$ for the $A.P. a, a + d, a + 2d, ...$
Hence, find the common difference of the A.P. for which,
$11^{th}$ term is 5 and $13^{th}$ term is 79.

Find the value of x such that PQ = QR where the coordinates of P, Q and R are (6, -1) , (1, 3) and (x, 8) respectively.

Find the missing frequencies in the following distribution, if the sum of the frequencies is $120$ and the mean is $50.$

Class	$0-20$	$20-40$	$40-60$	$60-80$	$80-100$
Frequency	$17$	$f_1$	$32$	$f_2$	$19$

A two-digit number is such that the product of its digits is 14. If 45 is added to the number, the digits interchange their places. Find the number.